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?

3.4 centimeters
10.6 centimeters
27.5 centimeters
29.2 centimeters

Answer 1

Answer: 27.5 centimeters

Explanation:

angle A measures 20 degrees and we know it's a write tringle so 180-(90+20)=70 degrees

so, angle B measures 70 degrees.

using the law of cosines:

`(sin70)/(b) =(sin20)/(10)`

`b=(10sin(70))/(sin(20))`

so, side b =
`(10sin(70))/(sin(20))`

Using the Pythagorean theorem to find the hypotenuse:

hypotenuse
`=\sqrt{((10 sin70)/(sin20))^(2) + 10^(2) }`

approximately = 27.5 centimeters