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

Answer:

D

Step-by-step explanation:

I took the test on E2020.

Answer 2

Answer:

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

Step-by-step 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

$y-x=53.56\°-36.44\°=17.12\°$