Heights and distances MCQs

Q1. Standing 45 m from a radio mast on flat ground, a surveyor measures the angle to its tip as 60 deg; what is the mast's height?

• A.22.5 m
• B.15*sqrt(3) m
• C.45 m
• D.45*sqrt(3) m

Answer: D. 45*sqrt(3) m

tan 60 = height/45, so height = 45*sqrt(3) m (since tan 60 = sqrt(3)).

Q2. Across a field 90 m wide, a fisherman views the lamp of a lighthouse at an elevation of 30 deg; how high is the lamp above his eye level?

• A.90 m
• B.90*sqrt(3) m
• C.30*sqrt(3) m
• D.45 m

Answer: C. 30*sqrt(3) m

height = 90 * tan 30 = 90/sqrt(3) = 30*sqrt(3) m.

Q3. A delivery rider parked 50 m from a telecom tower tilts his gaze 60 deg upward to its antenna; how far above the ground is the antenna?

• A.50*sqrt(3) m
• B.50 m
• C.25 m
• D.16.67*sqrt(3) m

Answer: A. 50*sqrt(3) m

height = 50 * tan 60 = 50*sqrt(3) m.