Question

Find the values of x and y.

Answer 1

x = 4
`√(6)` , y = 8
`√(2)`

Explanation:

Using the sine ratio in the right triangle on the left and the exact value

sin45° =
`(√(2) )/(2)`

let the altitude of the outer triangle be h ( common to both right triangles )

sin45° =
`(opposite)/(hypotenuse)` =
`(h)/(8)` =
`(√(2) )/(2)` ( cross- multiply )

2h = 8
`√(2)` ( divide both sides by 2 )

h = 4
`√(2)`

----------------------------------------------------------------

Using the tangent ratio in the right triangle on the right and the exact value

tan30° =
`(1)/(√(3) )` , then

tan30° =
`(opposite)/(adjacent)` =
`(h)/(x)` =
`(4√(2) )/(x)` =
`(1)/(√(3) )` ( cross- multiply )

x = 4
`√(6)`

--------------------------------------------------------------------

Using the sine ratio in the right triangle on the right and the exact value

sin30° =
`(1)/(2)` , then

sin30° =
`(h)/(y)` =
`(4√(2) )/(y)` =
`(1)/(2)` ( cross- multiply )

y =8
`√(2)`