Question

Please help me and explain the math.

Answer 1

The measure of ∠A = 58.0°

Explanation:

we will use the trigonometry function "tan" to solve the question

∵ BC is the opposite side of ∠A

∵ AC is the adjacent side of ∠A

∵ tan A =
`(opposite)/(adjacent)`

∴ tan A =
`(BC)/(AC)`

∵ BC = 8 units

∵ AC = 5 units

∴ tan A =
`(8)/(5)`

→ Use the inverse function of tan to find the measure of angle A

∵ m∠A =
`tan^(-1)((8)/(5))`

∴ m∠A = 57.99461679°

→ Round it to the nearest tenth

∴ m∠A = 58.0°

∴ The measure of ∠A = 58.0°