Question

In the figure shown below, m

A) x = 8tan 50°

B) x = 8cos 40°

C) x = 8sin 40°

D) x = 8tan 40°

Answer 1

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