How to find an angle with sine - ACT Math
Card 0 of 36
Simplify: (sinΘ + cosΘ)2
Simplify: (sinΘ + cosΘ)2
Using the foil method, multiply. Simplify using the Pythagorean identity sin2Θ + cos2Θ = 1 and the double angle identity sin2Θ = 2sinΘcosΘ.
Using the foil method, multiply. Simplify using the Pythagorean identity sin2Θ + cos2Θ = 1 and the double angle identity sin2Θ = 2sinΘcosΘ.
Compare your answer with the correct one above
For the triangle 
, find 
in degrees to the nearest integer
Note: The triangle is not necessarily to scale
For the triangle , find
Note: The triangle is not necessarily to scale
To solve this equation, it is best to remember the mnemonic SOHCAHTOA which translates to Sin = Opposite / Hypotenuse, Cosine = Adjacent / Hypotenuse, and Tangent = Opposite / Adjacent. Looking at the problem statement, we are given the side opposite of the angle we are trying to find as well as the hypotenuse. Therefore, we will be using the SOH part of our mnemonic. Inserting our values, this becomes 
. Then, we can write 
. Solving this, we get 
To solve this equation, it is best to remember the mnemonic SOHCAHTOA which translates to Sin = Opposite / Hypotenuse, Cosine = Adjacent / Hypotenuse, and Tangent = Opposite / Adjacent. Looking at the problem statement, we are given the side opposite of the angle we are trying to find as well as the hypotenuse. Therefore, we will be using the SOH part of our mnemonic. Inserting our values, this becomes
Compare your answer with the correct one above
A fifteen foot ladder is leaned up against a twelve foot building, reaching the top of the building. What is the angle made between the ladder and the ground? Round to the nearest hundredth of a degree.
A fifteen foot ladder is leaned up against a twelve foot building, reaching the top of the building. What is the angle made between the ladder and the ground? Round to the nearest hundredth of a degree.
You can draw your scenario using the following right triangle:
Recall that the sine of an angle is equal to the ratio of the oppositeside to the hypotenuse of the triangle. You can solve for the angle by using an inverse sine function:
or 
.
You can draw your scenario using the following right triangle:
Recall that the sine of an angle is equal to the ratio of the oppositeside to the hypotenuse of the triangle. You can solve for the angle by using an inverse sine function:
Compare your answer with the correct one above
What is the value of 
in the right triangle above? Round to the nearest hundredth of a degree.
What is the value of
Recall that the sine of an angle is equal to the ratio of the opposite side to the hypotenuse of the triangle. You can solve for the angle by using an inverse sine function:
or 
.
Recall that the sine of an angle is equal to the ratio of the opposite side to the hypotenuse of the triangle. You can solve for the angle by using an inverse sine function:
Compare your answer with the correct one above
Simplify: (sinΘ + cosΘ)2
Simplify: (sinΘ + cosΘ)2
Using the foil method, multiply. Simplify using the Pythagorean identity sin2Θ + cos2Θ = 1 and the double angle identity sin2Θ = 2sinΘcosΘ.
Using the foil method, multiply. Simplify using the Pythagorean identity sin2Θ + cos2Θ = 1 and the double angle identity sin2Θ = 2sinΘcosΘ.
Compare your answer with the correct one above
For the triangle , find in degrees to the nearest integer
Note: The triangle is not necessarily to scale
For the triangle , find
Note: The triangle is not necessarily to scale
To solve this equation, it is best to remember the mnemonic SOHCAHTOA which translates to Sin = Opposite / Hypotenuse, Cosine = Adjacent / Hypotenuse, and Tangent = Opposite / Adjacent. Looking at the problem statement, we are given the side opposite of the angle we are trying to find as well as the hypotenuse. Therefore, we will be using the SOH part of our mnemonic. Inserting our values, this becomes . Then, we can write . Solving this, we get
To solve this equation, it is best to remember the mnemonic SOHCAHTOA which translates to Sin = Opposite / Hypotenuse, Cosine = Adjacent / Hypotenuse, and Tangent = Opposite / Adjacent. Looking at the problem statement, we are given the side opposite of the angle we are trying to find as well as the hypotenuse. Therefore, we will be using the SOH part of our mnemonic. Inserting our values, this becomes
Compare your answer with the correct one above
A fifteen foot ladder is leaned up against a twelve foot building, reaching the top of the building. What is the angle made between the ladder and the ground? Round to the nearest hundredth of a degree.
A fifteen foot ladder is leaned up against a twelve foot building, reaching the top of the building. What is the angle made between the ladder and the ground? Round to the nearest hundredth of a degree.
You can draw your scenario using the following right triangle:
Recall that the sine of an angle is equal to the ratio of the oppositeside to the hypotenuse of the triangle. You can solve for the angle by using an inverse sine function:
or .
You can draw your scenario using the following right triangle:
Recall that the sine of an angle is equal to the ratio of the oppositeside to the hypotenuse of the triangle. You can solve for the angle by using an inverse sine function:
Compare your answer with the correct one above
What is the value of in the right triangle above? Round to the nearest hundredth of a degree.
What is the value of
Recall that the sine of an angle is equal to the ratio of the opposite side to the hypotenuse of the triangle. You can solve for the angle by using an inverse sine function:
or .
Recall that the sine of an angle is equal to the ratio of the opposite side to the hypotenuse of the triangle. You can solve for the angle by using an inverse sine function:
Compare your answer with the correct one above
Simplify: (sinΘ + cosΘ)2
Simplify: (sinΘ + cosΘ)2
Using the foil method, multiply. Simplify using the Pythagorean identity sin2Θ + cos2Θ = 1 and the double angle identity sin2Θ = 2sinΘcosΘ.
Using the foil method, multiply. Simplify using the Pythagorean identity sin2Θ + cos2Θ = 1 and the double angle identity sin2Θ = 2sinΘcosΘ.
Compare your answer with the correct one above
For the triangle , find in degrees to the nearest integer
Note: The triangle is not necessarily to scale
For the triangle , find
Note: The triangle is not necessarily to scale
To solve this equation, it is best to remember the mnemonic SOHCAHTOA which translates to Sin = Opposite / Hypotenuse, Cosine = Adjacent / Hypotenuse, and Tangent = Opposite / Adjacent. Looking at the problem statement, we are given the side opposite of the angle we are trying to find as well as the hypotenuse. Therefore, we will be using the SOH part of our mnemonic. Inserting our values, this becomes . Then, we can write . Solving this, we get
To solve this equation, it is best to remember the mnemonic SOHCAHTOA which translates to Sin = Opposite / Hypotenuse, Cosine = Adjacent / Hypotenuse, and Tangent = Opposite / Adjacent. Looking at the problem statement, we are given the side opposite of the angle we are trying to find as well as the hypotenuse. Therefore, we will be using the SOH part of our mnemonic. Inserting our values, this becomes
Compare your answer with the correct one above
A fifteen foot ladder is leaned up against a twelve foot building, reaching the top of the building. What is the angle made between the ladder and the ground? Round to the nearest hundredth of a degree.
A fifteen foot ladder is leaned up against a twelve foot building, reaching the top of the building. What is the angle made between the ladder and the ground? Round to the nearest hundredth of a degree.
You can draw your scenario using the following right triangle:
Recall that the sine of an angle is equal to the ratio of the oppositeside to the hypotenuse of the triangle. You can solve for the angle by using an inverse sine function:
or .
You can draw your scenario using the following right triangle:
Recall that the sine of an angle is equal to the ratio of the oppositeside to the hypotenuse of the triangle. You can solve for the angle by using an inverse sine function:
Compare your answer with the correct one above
What is the value of in the right triangle above? Round to the nearest hundredth of a degree.
What is the value of
Recall that the sine of an angle is equal to the ratio of the opposite side to the hypotenuse of the triangle. You can solve for the angle by using an inverse sine function:
or .
Recall that the sine of an angle is equal to the ratio of the opposite side to the hypotenuse of the triangle. You can solve for the angle by using an inverse sine function:
Compare your answer with the correct one above
Simplify: (sinΘ + cosΘ)2
Simplify: (sinΘ + cosΘ)2
Using the foil method, multiply. Simplify using the Pythagorean identity sin2Θ + cos2Θ = 1 and the double angle identity sin2Θ = 2sinΘcosΘ.
Using the foil method, multiply. Simplify using the Pythagorean identity sin2Θ + cos2Θ = 1 and the double angle identity sin2Θ = 2sinΘcosΘ.
Compare your answer with the correct one above
For the triangle , find in degrees to the nearest integer
Note: The triangle is not necessarily to scale
For the triangle , find
Note: The triangle is not necessarily to scale
To solve this equation, it is best to remember the mnemonic SOHCAHTOA which translates to Sin = Opposite / Hypotenuse, Cosine = Adjacent / Hypotenuse, and Tangent = Opposite / Adjacent. Looking at the problem statement, we are given the side opposite of the angle we are trying to find as well as the hypotenuse. Therefore, we will be using the SOH part of our mnemonic. Inserting our values, this becomes . Then, we can write . Solving this, we get
To solve this equation, it is best to remember the mnemonic SOHCAHTOA which translates to Sin = Opposite / Hypotenuse, Cosine = Adjacent / Hypotenuse, and Tangent = Opposite / Adjacent. Looking at the problem statement, we are given the side opposite of the angle we are trying to find as well as the hypotenuse. Therefore, we will be using the SOH part of our mnemonic. Inserting our values, this becomes
Compare your answer with the correct one above
A fifteen foot ladder is leaned up against a twelve foot building, reaching the top of the building. What is the angle made between the ladder and the ground? Round to the nearest hundredth of a degree.
A fifteen foot ladder is leaned up against a twelve foot building, reaching the top of the building. What is the angle made between the ladder and the ground? Round to the nearest hundredth of a degree.
You can draw your scenario using the following right triangle:
Recall that the sine of an angle is equal to the ratio of the oppositeside to the hypotenuse of the triangle. You can solve for the angle by using an inverse sine function:
or .
You can draw your scenario using the following right triangle:
Recall that the sine of an angle is equal to the ratio of the oppositeside to the hypotenuse of the triangle. You can solve for the angle by using an inverse sine function:
Compare your answer with the correct one above
What is the value of in the right triangle above? Round to the nearest hundredth of a degree.
What is the value of
Recall that the sine of an angle is equal to the ratio of the opposite side to the hypotenuse of the triangle. You can solve for the angle by using an inverse sine function:
or .
Recall that the sine of an angle is equal to the ratio of the opposite side to the hypotenuse of the triangle. You can solve for the angle by using an inverse sine function:
Compare your answer with the correct one above
Simplify: (sinΘ + cosΘ)2
Simplify: (sinΘ + cosΘ)2
Using the foil method, multiply. Simplify using the Pythagorean identity sin2Θ + cos2Θ = 1 and the double angle identity sin2Θ = 2sinΘcosΘ.
Using the foil method, multiply. Simplify using the Pythagorean identity sin2Θ + cos2Θ = 1 and the double angle identity sin2Θ = 2sinΘcosΘ.
Compare your answer with the correct one above
For the triangle , find in degrees to the nearest integer
Note: The triangle is not necessarily to scale
For the triangle , find
Note: The triangle is not necessarily to scale
To solve this equation, it is best to remember the mnemonic SOHCAHTOA which translates to Sin = Opposite / Hypotenuse, Cosine = Adjacent / Hypotenuse, and Tangent = Opposite / Adjacent. Looking at the problem statement, we are given the side opposite of the angle we are trying to find as well as the hypotenuse. Therefore, we will be using the SOH part of our mnemonic. Inserting our values, this becomes . Then, we can write . Solving this, we get
To solve this equation, it is best to remember the mnemonic SOHCAHTOA which translates to Sin = Opposite / Hypotenuse, Cosine = Adjacent / Hypotenuse, and Tangent = Opposite / Adjacent. Looking at the problem statement, we are given the side opposite of the angle we are trying to find as well as the hypotenuse. Therefore, we will be using the SOH part of our mnemonic. Inserting our values, this becomes
Compare your answer with the correct one above
A fifteen foot ladder is leaned up against a twelve foot building, reaching the top of the building. What is the angle made between the ladder and the ground? Round to the nearest hundredth of a degree.
A fifteen foot ladder is leaned up against a twelve foot building, reaching the top of the building. What is the angle made between the ladder and the ground? Round to the nearest hundredth of a degree.
You can draw your scenario using the following right triangle:
Recall that the sine of an angle is equal to the ratio of the oppositeside to the hypotenuse of the triangle. You can solve for the angle by using an inverse sine function:
or .
You can draw your scenario using the following right triangle:
Recall that the sine of an angle is equal to the ratio of the oppositeside to the hypotenuse of the triangle. You can solve for the angle by using an inverse sine function:
Compare your answer with the correct one above
What is the value of in the right triangle above? Round to the nearest hundredth of a degree.
What is the value of
Recall that the sine of an angle is equal to the ratio of the opposite side to the hypotenuse of the triangle. You can solve for the angle by using an inverse sine function:
or .
Recall that the sine of an angle is equal to the ratio of the opposite side to the hypotenuse of the triangle. You can solve for the angle by using an inverse sine function:
Compare your answer with the correct one above