Question

Lines (1) and (2) are parallel. Find sides M and N. Round your answer to the nearest tenth.

Answer 1

To determine the values of M and N in the given right triangle we need first to determine the value of angle P. Angle P is equal to the supplementary angle of the 152° angle, that is:

$152+\angle z=180$

Solving for angle z:

$\angle z=180-152=28$

To determine the value of N we can use the function sine since this function is defined as:

$\sin x=\frac{opposite}{hypotenuse}$

REplacing the known values:

$\sin 28=\frac{N}{9}$

Solving for N by multiplying both sides by 9:

$9\sin 28=N$

Solving the operation:

$4.2=N$

To determine the value of M we can use the function cosine since this function is defined as:

$\cos x=\frac{adjacent}{hypotenuse}$

Replacing the known values:

$\cos 28=\frac{M}{9}$

Multiplying both sides by 9:

$9\cos 28=M$

Solving the operation:

$7.9=M$