Mathematics, 28.07.2019 04:33 maqle

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.

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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 from: Kencharlot

The length of side LM is 20.9 feet

The side lengths and measure of angles are given as;

Angle N = 90 degreesAngle M = 17 degreesLength 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

Read more about right-triangles at:

link

Answer from: Quest

100 kilometers per piles hour

Answer from: Quest

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