High School Math : Acute / Obtuse Triangles
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Example Questions
Example Question #2 : Acute / Obtuse Triangles
Points A, B, and C are collinear (they lie along the same line). The measure of angle CAD is 
Find the measure of 
The measure of 
Because the measures of the three angles in a triangle must add up to 
Example Question #2 : Acute / Obtuse Isosceles Triangles
The base angle of an isosceles triangle is 
Every triangle has 180 degrees. An isosceles triangle has one vertex angle and two congruent base angles.
Solve the equation 
x = 180 - 27 - 27
x = 126
Therefore the measure of the vertex angle is 
Example Question #61 : Triangles
An isosceles triangle has an area of 12. If the ratio of the base to the height is 3:2, what is the length of the two equal sides?
4
6
4√3
5
3√3
5
Area of a triangle is ½ x base x height. Since base:height = 3:2, base = 1.5 height. Area = 12 = ½ x 1.5 height x height or 24/1.5 = height2. Height = 4. Base = 1.5 height = 6. Half the base and the height form the legs of a right triangle, with an equal leg of the isosceles triangle as the hypotenuse. This is a 3-4-5 right triangle.
Example Question #62 : Triangles
Two sides of a triangle each have length 6. All of the following could be the length of the third side EXCEPT
This question is about the Triangle Inequality, which states that in a triangle with two sides A and B, the third side must be greater than the absolute value of the difference between A and B and smaller than the sum of A and B.
Applying the Triangle Inequality to this problem, we see that the third side must be greater than the absolute value of the difference between the other two sides, which is |6-6|=0, and smaller than the sum of the two other sides, which is 6+6=12. The only answer choice that does not satisfy this range of possible values is 12 since the third side must be LESS than 12.
Example Question #62 : Triangles
Find the area of a triangle whose base is 
This problem is solved using the geometric formula for the area of a triangle.
Convert feet to inches.
Example Question #141 : Sat Mathematics
If triangle ABC has vertices (0, 0), (6, 0), and (2, 3) in the xy-plane, what is the area of ABC?
18
12
10
20
9
9
Sketching ABC in the xy-plane, as pictured here, we see that it has base 6 and height 3. Since the formula for the area of a triangle is 1/2 * base * height, the area of ABC is 1/2 * 6 * 3 = 9.
Example Question #61 : Triangles
What is the area of a triangle with a height of 
When searching for the area of a triangle we are looking for the amount of the space enclosed by the triangle.
The equation for area of a triangle is
Plug the values for base and height into the equation yielding
Then multiply the numbers together to arrive at the answer 
Example Question #1 : How To Find The Area Of An Acute / Obtuse Triangle
The height, 
If 
Using the formula for the area of a triangle (
Example Question #1 : How To Find The Length Of The Side Of An Acute / Obtuse Triangle
A triangle has a perimeter of 36 inches, and one side that is 12 inches long. The lengths of the other two sides have a ratio of 3:5. What is the length of the longest side of the triangle?
9
14
12
15
8
15
We know that the perimeter is 36 inches, and one side is 12. This means, the sum of the lengths of the other two sides are 24. The ratio between the two sides is 3:5, giving a total of 8 parts. We divide the remaining length, 24 inches, by 8 giving us 3. This means each part is 3. We multiply this by the ratio and get 9:15, meaning the longest side is 15 inches.
Example Question #1 : How To Find The Length Of The Side Of An Acute / Obtuse Triangle
A triangle has sides of length 8, 13, and L. Which of the following cannot equal L?
6
15
9
7
4
4
The sum of the lengths of two sides of a triangle cannot be less than the length of the third side. 8 + 4 = 12, which is less than 13.
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