Question

1. in the right triangle, the hypotenuse is 10, one acute angle is 60°, the other acute angle is 30°, find the lengths of the right - angled sides x and y.

Explanation:

Step1: Find side $x$ (opposite 60°)

Use sine of 60°:
$\sin(60^\circ) = \frac{x}{10}$
$x = 10 \times \sin(60^\circ) = 10 \times \frac{\sqrt{3}}{2} = 5\sqrt{3}$

Step2: Find side $y$ (adjacent to 60°)

Use cosine of 60°:
$\cos(60^\circ) = \frac{y}{10}$
$y = 10 \times \cos(60^\circ) = 10 \times \frac{1}{2} = 5$

Answer:

$x = 5\sqrt{3}$, $y = 5$