Question

HELP ME PLEASE SOLVE THE TRIANGLE BELOW FOR Y

Answer 1

Explanation:

`tan30=(4)/(y)`

So

`y=(4)/(tan 30) =(4)/((√(2) )/(2) )=(8)/(√(2) )*(√(2) )/(√(2) )=(8√(2) )/(2)=4√(2)`

For X we have:

`sin30=(4)/(x)`

`X=(4)/(sin30)=(4)/((1)/(2) )=(4*2)/(1*1)=8`

Answer 2

x = 8 , y = 4
`√(3)`

Explanation:

using the sine/ cosine ratios in the right triangle and the exact values

sin30° =
`(1)/(2)` and cos30° =
`(√(3) )/(2)` , then

sin30° =
`(opposite)/(hypotenuse)` =
`(4)/(x)` =
`(1)/(2)` ( cross- multiply )

x = 4 × 2 = 8

Then

cos30° =
`(adjacent)/(hypotenuse)` =
`(y)/(x)` =
`(y)/(8)` =
`(√(3) )/(2)` ( cross- multiply )

2y = 8
`√(3)` ( divide both sides by 2 )

y = 4
`√(3)`