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=(10)/(x) \\ \\ x * \sin 20^\circ = 10 \\ \\ x = (10)/(\sin 20^\circ) \\ \\ x \approx (10)/(0.342) \\ \\ x \approx 29.2`

The hypotenuse is approximately 29.2 cm long.

Answer 2

29.23 cm

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 = (Perpendicular)/(Hypotenuse)`

`Sin 20^(\circ) = (BC)/(AC)`

`0.3420 = (10)/(AC)`

`AC= (10)/(0.3420)`

`AC= 29.23`

Thus the hypotenuse of given triangle is approximately 29.23 cm.