Question

Triangle L M N is shown. Angle N L M is a right angle. The length of N L is 19.1 inches and the length of L M is 14.1 inches. Angle L N M is x and angle N M L is y. What is the approximate value of y − x?

Answer 1

The approximate value of (y − x) is
`17.12\°`

Explanation:

step 1

Find the measure of angle NML

y=m∠NML

`tan(y)=NL/LM` ---> opposite side to angle y divided by the adjacent side to angle y

see the attached figure to better understand the problem

substitute the given value

`tan(y)=19.1/14.1`

`y=tan^(-1)(19.1/14.1)=53.56\°`

step 2

Find the measure of angle LNM

x=m∠LNM

we know that

`x+y=90\°` -----> by complementary angles

solve for x

`x+53.56\°=90\°`

`x=90\°-53.56\°=36.44\°`

step 3

Find the approximate value of y-x

we have

`y=53.56\°`

`x=36.44\°`

so

`y-x=53.56\°-36.44\°=17.12\°`