Question

Angle A is an acute angle. Use a calculator to approximate the measure of A. Round decimals to one place.
Tan A = 2.50
m∠A ≈ º

Answer 1

The measure of angle A is $\angle A=68.2^{\circ}$

Explanation:

Given that the angle A is an acute angle.

Also, given that $tan \ A=2.50$

Measure of angle A:

We need to determine the measure of angle A.

Since, we have,

$tan \ A=2.50$

Let us multiply $tan^{-1}$ on both sides of the equation.

Thus, we get,

$(tan^{-1})tan \ A=tan^{-1} (2.50)$

Simplifying the terms, we have,

$A=tan^{-1} (2.50)$

Using calculator, we shall determine the measure of A.

Substituting $\tan ^{-1}(2.50)=68.19859051$, we get,

$A=68.19859051$

Rounding off the decimal to one place, we have,

$A=68.2$

Hence, the measure of angle A is $\angle A=68.2^{\circ}$