Question

In Triangle PQR, the measure of ZR=90°, the measure of ZP=51°, and QR = 38 feet. Find the length of PQ to the nearest tenth of a foot.

Answer 1

Answer:

Therefore Length of PQ is 48.9 foot.

Step-by-step explanation:

Given:

In Triangle PQR,

∠R = 90°

∠P = 51°

QR = 38 feet = side opposite to angle P

To Find:

PQ = ? = Hypotenuse

Solution:

In Right angle Triangle PQR Cosine Identity we get,

$\sin P = \dfrac{\textrm{side opposite to angle P}}{Hypotenuse}$

Substituting the values we get,

$\sin 51 = \dfrac{QR}{PQ}=\dfrac{38}{PQ}\\\\0.7771=\dfrac{38}{PQ}\\\\PQ=\dfrac{38}{0.7771}=48.899\\\\\therefore PQ=48.9\ foot$

Therefore Length of PQ is 48.9 foot.