Question

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.

Answer 1

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. 
$cos \theta = \frac{adj}{hyp}$
plug in known values
$cos(17) = \frac{20}{x}$
switch cos(20) and x using the products property
$x = \frac{20}{cos(17)}$
plug into calculator to get 20.9 ft

Answer 2

The length of side LM is 20.9 feet

The side lengths and measure of angles are given as;

• Angle N = 90 degrees
• Angle M = 17 degrees
• Length MN = 20 feet

The 90 degrees at point N means that the triangle is a right-triangle.

So, side length LM is calculated using the following cosine ratio

$\cos(M) = \frac{MN}{LM}$

Substitute known values in the above equation

$\cos(17) = \frac{20}{LM}$

Make LM the subject

$LM = \frac{20}{\cos(17)}$

Evaluate cos(17 degrees)

$LM = \frac{20}{0.9563}$

Evaluate the quotient

$LM = 20.9$

Hence, the value of LM is 20.9 feet

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