Question

From the top of a tower of height 40 feet, the angles of depression of two objects south and north of the tower are both 45°. What is the distance between the two objects (in feet)?

A 40√2 Correct Answer Incorrect Answer
B 80 Correct Answer Incorrect Answer
C 80√2 Correct Answer Incorrect Answer
D 160 Correct Answer Incorrect Answer

Solution

In ΔABC, tan 45° = 40/CB ⇒ 1 = 40/CB ⇒ CB = 40 feet In ΔABD, tan 45° = 40/BD ⇒ 1 = 40/BD ⇒ BD = 40 feet CD = CB + BD = 40 + 40 = 80 feet

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