Question

City A is 350 miles due south of City B. City C is 500 miles due east of City B. What is the measure of ∠C to the nearest degree?
a. 35˚ b. 44˚ c. 55˚ d. 90˚

Answer 1

Tan C = 350 / 500
tan C = 0.7
∠ C = tan^(-1) 0.7
∠ C = 34.99° ≈ 35°
Answer:
The measure of angle C is
A. 35°

Answer 2

From the given figure,

$\tan C= \frac{350}{500} =0.7 \\ \\ \Rightarrow C=\tan^{-1}(0.7)\approx35^o$