Question

What is the measure of angle A?

Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.

[ ° ]

Answer 1

77.32

Explanation:

sin = opposite/hypotenuse

Opposite of A = BC = 80

Hypotenuse = AC = 82

sin A = 80/82

Use a calculator: A = 77.32

Answer 2

Answer: The measure of angle A is 77.32°.

Step-by-step explanation: We are given to find the measure of angle A from the figure provided.

From the figure, we can note that

ΔABC is a right-angled triangle, where

∠B = 90°, AB = 18 units , BC = 80 units and hypotenuse AC = 82 units.

Therefore, from the laws of ratios of trigonometry we have

`\sin m\angle A=(perpendicular)/(hypotenuse)\\\\\\\Rightarrow \sin m\angle A=(80)/(82)\\\\\\\Rightarrow \sin m\angle A=0.9756\\\\\Rightarrow m\angle A=\sin^(-1)(0.9756)\\\\\Rightarrow m\angle A=77.3170^\circ\sim 77.32^\circ.`

Thus, the measure of angle A is 77.32°.