Answer :
Final answer:
To find the measure of angle A, we use the given values and formulas deriving an approximate angle of 36.6 degrees. Comparing this to the given options, the closest match is option C, thus the measure of angle A is 36.9 degrees.
Explanation:
To measure the angle A, we should break down the problem step-by-step. First, from the provided information, we know that A = 53.0 m and θB = 63.0°. To find the components of A, we use Ax = A cos θ, which gives Ax = 49.2 m.
Next, using given the equation θ = tan¯¹(0.742) we calculate to get θ = 36.6 °. This suggests that angle A, when measured, is approximately 36.6 degrees.
However, because we are choosing the correct answer from the provided options (A) 35.2 degrees, (B) 53.1 degrees, (C) 36.9 degrees, (D) 45 degrees, the closest and thus correct choice would be (C) 36.9 degrees.
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