Question

In a right triangle, angle A measures 20°. The side opposite angle A is 10 centimeters long. Approximately how long is the hypotenuse of the triangle?

Answer 1

The sine of angle A is the length of the side opposite to the angle divided by the length of the hypotenuse.
$\sin 20^\circ=\frac{10}{x} \\ \\ x \times \sin 20^\circ = 10 \\ \\ x = \frac{10}{\sin 20^\circ} \\ \\ x \approx \frac{10}{0.342} \\ \\ x \approx 29.2$

The hypotenuse is approximately 29.2 cm long.

Answer 2

Answer:

29.23 cm

Step-by-step explanation:

Given : In a right triangle, angle A measures 20°. The side opposite angle A is 10 centimeters long.

To Find: Approximately how long is the hypotenuse of the triangle?

Solution:

Refer the Attached figure

In ΔABC

BC = 10 cm

∠A = 20°

AC = Hypotenuse

Using trigonometric ratio

$Sin \theta = \frac{Perpendicular}{Hypotenuse}$

$Sin 20^{\circ} = \frac{BC}{AC}$

$0.3420 = \frac{10}{AC}$

$AC= \frac{10}{0.3420}$

$AC= 29.23$

Thus the hypotenuse of given triangle is approximately 29.23 cm.