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.

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. 

plug in known values

switch cos(20) and x using the products property

plug into calculator to get 20.9 ft

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

Substitute known values in the above equation

Make LM the subject

Evaluate cos(17 degrees)

Evaluate the quotient

Hence, the value of LM is 20.9 feet

Read more about right-triangles at:

link

3(x + 2y = 9) = 3x + 6y = 27 < I multiplied this equation by 3 to get the y value to cancel with the y value of the next equation

2(-x - 3y = -14) = -2x - 6y = -28 , I multiplied this equation by 2 to get the y value to cancel with the y value of the previous equation

   3x + 6y = 27

+ 2x  - 6y = -28

5x             = 55
             x  = 55/5
             x = 11

Then plug the 11 into one of the equations to solve for y.

x + 2y = 9
(11) + 2y = 9
           2y = 9 - 11
           2y = -2
             y = -2/2
             y = -1

hope this helps :)