Hello from MrBillDoesMath!
Answer:
Choice A, x = 8 tan 50
Discussion:
The hypotenuse is not shown int he figure suggesting we need a trig ratio that doesn't use it!. Tan comes to mind as
tan(x) = side opposite / side adjacent => in our case
tan(40) = 8/x => multiply both sides by x
x * tan(40) = 8 =>
x = 8/ tan(40)
Oops!. That answer if not provided (sorry about that) but it's stilla good try. Let's apply the same idea to the other angle in the triangle. That is angle A. As a triangle contains 180 degrees
angle A + 90 + 40 = 180
angle A = 180 - 90 - 40
= 180 - 130
= 50
So, once again,
tan(50) = x/8 => multiply both sides by 8
8 tan(50) = x
which is Choice A.
Thank you,
MrB
