Trigonometry : Right Triangles
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Example Questions
Example Question #1 : 45 45 90 Triangles
In a 
One option is to use the Pythagorean Theorem.
Since we have an isosceles triangle, both legs must be congruent.
Plug in to get your answer.
Or, you can remember the 45-45-90 identity, which states that the hypotenuse is 
Example Question #2 : 45 45 90 Triangles
In a 45-45-90 triangle, if the hypotenuse is 10, what is the perimeter of the triangle?
Write the Pythagorean Theorem.
In a 45-45-90 triangle, the length of the legs are equal, which indicates that:
Rewrite the formula and substitute the known sides.
The lengths of the triangle are:
Sum the three lengths for the perimeter.
Example Question #3 : 45 45 90 Triangles
One side of a 
If 3 is one of the legs, then the hypotenuse is 
If 3 is the hypotenuse, then the legs are 
Example Question #4 : 45 45 90 Triangles
The hypotenuse of a 
Divide the length of the hypotenuse by 
Example Question #5 : 45 45 90 Triangles
The perimeter of a square is 56 feet. What is the length of the diagonal in feet?
There is not enough information
The perimeter of a square can be found using the formula 
The diagonal of a square forms the hypotenuse of a 45-45-90 triangle, where each leg is the side of the square. In a 45-45-90 triangle, the ratio of the hypotenuse to the leg is 
Example Question #1 : 45 45 90 Triangles
Find the value of
Solving this problem begins with realizing that all three of our triangles are not only right triangles but isosceles and are therefore 45-45-90 triangles. That means in each triangle to get from the length of a leg to the length of the hypotenuse, we simply multiply by 
However, the hypotenuse of the bottom triangle is also the leg of the middle triangle. To find the hypotenuse of this triangle, we simply repeat the process.
However, again the hypotenuse of the middle triangle is also the leg of the upper triangle. To find 
Example Question #1 : 30 60 90 Triangles
In a 30-60-90 triangle, the length of the side opposite the 
By definition, the length of the hypotenuse is twice the length of the side opposite the 
Recall that the hypotenuse is the side opposite the 
Thus, using the equation below, where ss represents the short side (that opposite the 
Plugging in our values for the short side we find the hypotenuse as follows:
Example Question #271 : Trigonometry
A triangle has three angles 
A triangle with a 
Therefore, to make the above statement true 
Example Question #271 : Trigonometry
Triangle 
What is the height of the triangle?
An equilateral triangle has internal angles of 60°, so the sin of one of those angles is equivalent to the height of the triangle divided by the side length,
so..
Example Question #11 : Triangles
In a 
Based on the 30-60-90 identity, the measure of the side opposite the 30 degree angle is doubled to get the hypotenuse.
Therefore,
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