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?

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 Link

wifilethbridge wifilethbridge · Answer 2 · 2019-05-15T03:44:39-04:00

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.