Find Side q in 45-45-90 Right Triangle

Published on March 12, 2026

Geometry

Determine the length of leg q in a 45-45-90 triangle where the hypotenuse is s2, using the properties of isosceles right triangles or trigonometry.

Question

Answer

Here is the step-by-step solution to find the value of

1. Analyze the Triangle

The image shows a triangle with the following known properties:

Two angles are each.
One angle is marked with a square, indicating it is a right angle, which means it measures .

The sum of the angles in any triangle must be

. Let the third angle be

Wait, let’s re-examine the image. The image shows two angles marked as

and one angle marked as

(the right angle symbol). This configuration (

) defines a special type of right triangle: a

triangle, which is also an isosceles right triangle.

2. Properties of a -- Triangle

In a

triangle, the two legs (the sides opposite the

angles) are equal in length.
The relationship between the leg length (

) and the hypotenuse (

) is:

3. Identify Sides in the Given Triangle

The sides opposite the angles are the legs.
The side opposite the angle is the hypotenuse.

From the diagram:

One leg is labeled .
The other leg is not explicitly labeled, but since it is opposite a angle, it must be equal to .
The side labeled is opposite the angle, so it is the hypotenuse.

Therefore, we have:

Leg
Hypotenuse

4. Set up the Equation

Using the relationship

where

and

5. Solve for

To find

, divide both sides by

Alternatively, using trigonometry (SOH CAH TOA):
If we use the

angle adjacent to side

Side is the Adjacent side.
Side is the Hypotenuse (opposite the angle).
We use the Cosine function:

We know that

Multiply both sides by

The value of

. Since the answer must be in simplest radical form,

is acceptable (it is

or just

The answer is

units.

🚀 Try Free Math Help Now!🏠 Learn More Powerful Features

Find Side q in 45-45-90 Right Triangle

Question

Answer

Related math solutions

Web版を永久に解除

Related math solutions