In the figure shown below, m a) x = 8tan 50° b) x = 8cos 40° c) x = 8sin 40° d) x = 8tan 40°

Hello from MrBillDoesMath!

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

a. is correct