Question

What is measure of angle A? Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth. ° Right triangle A B C, with right angle C B A. Side A B is three centimeters, side B C is four centimeters, and side C A is five centimeters.

Answer 1

Answer: 53.13 is the answer.

Explanation:

Answer 2

The measure of angle A is 53.13°.

Explanation:

Given,

ABC is a triangle,

In which m∠CBA = 90°, AB = 3 cm, BC = 4 cm and CA = 5 cm,

By the law of sine,

`(sinA)/(BC)=(sinB)/(AC)`

`sin A = BC* (sin B)/(AC)` ( By cross multiplication )

By substituting the values,

`sin A = 4* (sin 90^(\circ))/(5)`

`sin A = (4)/(5)` ( sin 90° = 1 )

`m\angle A = sin^(-1)((4)/(5))`

`\implies m\angle A =53.1301023542^(\circ)\approx 53.13^(\circ)`

Hence, the measure of angle A is 53.13°.