Final answer:
To find the measure of ∠A, use the inverse tangent function with the ratio of the opposite side (10 cm) to the adjacent side (12 cm) of the right triangle.
Step-by-step explanation:
To determine the measure of ∠A using inverse tangent in a triangle with side lengths of 10 cm and 12 cm (assuming this is a right triangle where these are the two legs), we must employ the concept of trigonometric functions. The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side.
Therefore, if ∠A is opposite the side with length 10 cm and adjacent to the side with length 12 cm, we can find ∠A by using the formula:
tan⁻¹(opposite/adjacent)
Applying the formula, we get:
∠A = tan⁻¹(10/12)
The use of an inverse trigonometric function, specifically tan⁻¹, allows us to calculate the angle when we know the sides.