Trigonometry question

Question

To find the distance across a small lake, a surveyor has taken the measurements shown. Find the distance across the lake using this information. Enter your answer as a number; your answer should be accurate to 2 decimal places

Numbers provided on diagram 1.74 mi, 29.7°, 2.36 mi

Answer 1

Assuming that the diagram is a triangle with unknown side, call it x, which is the side opposite the given angle, use the Law of Cosines:

x² = (1.74)² + (2.36)² - 2(1.74)(2.36)cos29.7°

x² = 8.5972 - 8.2182cos29.7°

x² = 8.5972 - 7.1339

x² = 1.4633

x ≈ 1.21 miles