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=(opposite)/(hypotenuse)`

REplacing the known values:

`\sin 28=(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=(adjacent)/(hypotenuse)`

Replacing the known values:

`\cos 28=(M)/(9)`

Multiplying both sides by 9:

`9\cos 28=M`

Solving the operation:

`7.9=M`