Question

find pq.

(image of a right triangle prq with right angle at r, rq = √42, angle at q is 31°)

write your answer as an integer or as a decimal rounded to the nearest tenth.
pq =
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work it out
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Explanation:

Step1: Identify adjacent side to $\angle Q$

The side adjacent to $31^\circ$ is $RQ = \sqrt{42}$, and $\cos(Q) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{RQ}{PQ}$.

Step2: Rearrange to solve for $PQ$

$PQ = \frac{\sqrt{42}}{\cos(31^\circ)}$

Step3: Calculate values

First, $\sqrt{42} \approx 6.4807$, $\cos(31^\circ) \approx 0.8572$. Then $\frac{6.4807}{0.8572} \approx 7.6$.

Answer:

$7.6$