Question

In triangle ABC, the measure of ∠B is 90°, AC = 50°, AB= 48°, and BC= 14°. Which ratio represents the tangent of ∠A.

A) tan(A) = 48/14
B) tan(A) = 14/48
C) tan(A) = 48/50
D) tan(A) = 50/48

Answer 1

There appears to be a typo in the student's question, as they provided angle measures that cannot possibly form a triangle.

Step-by-step explanation:

To find the ratio representing the tangent of ∠A in a right triangle where ∠B is 90°, we need to refer to triangle ABC with the given angles. However, there seems to be a discrepancy in the question as the sum of angles provided for triangle ABC exceeds 180°, which is not possible for a triangle. Assuming the typo refers to the lengths of sides AB and BC instead of being angles, and AC represents the angle at C, we can proceed.

In trigonometry, the tangent of an angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side. Since ∠B is the right angle, ∠A would be opposite side AB and adjacent to side BC. Therefore, the tangent of ∠A is the ratio of AB to BC.

The correct ratio for tan(A) would be AB/BC, which corresponds to 48/14, thus option A) tan(A) = 48/14 is the correct choice assuming that AB and BC represent the lengths of the sides.