In ΔLMN, the measure of ∠N=90°, the measure of ∠M=17°, and MN = 20 feet. Find the length of LM to the nearest tenth of a foot.

Accepted Solution

20.9 ft
This is a right triangle trigonometry question because N is 90 degrees. MN is adjacent to M and LM is the hypotenuse. Adjacent any hypotenuse use the cosine function. 
[tex]cos \theta = \frac{adj}{hyp}[/tex]
plug in known values
[tex]cos(17) = \frac{20}{x}[/tex]
switch cos(20) and x using the products property
[tex]x = \frac{20}{cos(17)}[/tex]
plug into calculator to get 20.9 ft