You are walking near a river. While standing at A, you measure an angle of 90° between B and C, as shown. You then walk to B and measure an angle of 77° between A and C. The distance between A and B is about 1.5 miles. How wide (in miles) is the river between A and C? Round your answer to the nearest tenth.

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Answer:

Length of AC = 6.67 miles

Step-by-step explanation:

Given:

Angel between B and C = 90°

Angel between A and C = 77°

AB = 1.5 miles

Find:

Length of AC

Computation:

Using trigonometric laws

Cos 77° =  Base / hypotenuses

0.225 = 1.5 / hypotenuses

hypotenuses = 6.67 miles

Length of AC = 6.67 miles

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