Question

1. here is triangle pqr. find the length of each leg.

(image of right triangle pqr with right angle at q, angle at r is 30°, angle at p is 60°, hypotenuse pr is length 4)

Explanation:

Step1: Identify hypotenuse length

Hypotenuse $PR = 4$

Step2: Calculate leg $QR$ (opposite 60°)

Use $\sin(60^\circ)=\frac{QR}{PR}$
$\sin(60^\circ)=\frac{\sqrt{3}}{2}$, so $QR = 4 \times \frac{\sqrt{3}}{2} = 2\sqrt{3}$

Step3: Calculate leg $PQ$ (opposite 30°)

Use $\sin(30^\circ)=\frac{PQ}{PR}$
$\sin(30^\circ)=\frac{1}{2}$, so $PQ = 4 \times \frac{1}{2} = 2$

Answer:

Length of leg $PQ = 2$, Length of leg $QR = 2\sqrt{3}$