Question

Find the values of x and y. Write all radicals in simplest form.

Answer 1

For the 60-30-90 degree triangle:

x=12

y=
`12√(3)`

For the 30-60-90 degree triangle:

x=16

y=
`8√(3)`

For the 45-45-90 degree triangle:

x=7

y=
`7√(2)`

Explanation:

For 30-60-90 triangles, the side opposite the 30 degree angle is x, while the side opposite the hypotenuse is 2x, while the side opposite the 60 degree angle is
`x√(3)`.

For 45-45-90 triangles, the sides opposite the 45 degree angles are x, while the hypotenuse is
`x√(2)`.