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.

Step-by-step explanation:

Answer 2

Answer:

The measure of angle A is 53.13°.

Step-by-step 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,

$\frac{sinA}{BC}=\frac{sinB}{AC}$

$sin A = BC\times \frac{sin B}{AC}$ ( By cross multiplication )

By substituting the values,

$sin A = 4\times \frac{sin 90^{\circ}}{5}$

$sin A = \frac{4}{5}$               ( sin 90° = 1 )

$m\angle A = sin^{-1}(\frac{4}{5})$          

$\implies m\angle A =53.1301023542^{\circ}\approx 53.13^{\circ}$

Hence, the measure of angle A is 53.13°.