Question

For the right triangles below, find the exact values of the side lengths c and d.

If necessary, write your responses in simplified radical form.

Answer 1

c = 7
`√(2)`, d = 4/
`√(3)`

Explanation:

The first triangle is a 45-45-90 triangle, meaning the two sides adjacent to the right angle are equal to the same value, while the side opposite the right angle is equal to one of the other sides times
`√(2)`.

The second triangle is a 30-60-90 triangle, meaning the side opposite the 30 degree angle is equal to x, the side opposite the 60 degree angle is equal to x
`√(3)`, and the side opposite the right angle is equal to 2x. Since the side opposite the 60 degree angle is 4, we know that x times
`√(3)` is equal to 4. Therefore, x is 4/
`√(3)`. The side opposite the 90 degree angle is 2x, and therefore, 8/
`√(3)`.