Question

3. Find the missing side lengths. Leave the answers as radicals in simplest form.

Answer 1

x = y = 6.5
`√(2)`

Explanation:

the triangle is isosceles, both base angles are 45° then the 2 legs are congruent , that is x = y

using the sine ratio in the right triangle and the exact value

sin45° =
`(√(2) )/(2)` , then

sin45° =
`(opposite)/(hypotenuse)` =
`(x)/(13)` =
`(√(2) )/(2)` ( cross- multiply )

2x = 13
`√(2)` ( divide both sides by 2 )

x = y = 6.5
`√(2)`