Trigonometry word problem (basic trig)

Question

From a boat on the water the angle of elevation of the top of a cliff is 30 degrees. From a point 400m closer to the cliff, the angle of elevation is 35 degrees. Find the height of the cliff

Answer 1

First, draw yourself a picture, it always helps.  Second, remember that angle of elevation (or depression) is ALWAYS measured with respect to the horizontal.  Label your picture.  I chose h for the height of the cliff, and x for the distance from the second vantage point to the cliff.  This gives me two equations, since I know that tan A = opposite/adjacent.

 

1. tan 30 = h/(400+x)
2. tan 35 = h/x

 

Two equations, two unknowns, so we can solve this

 

• h=xtan35
• h=.7x
• tan30 = h/(400+x)
• .577=(.7x)/(400+x)
• .577(400+x)=.7x
• 230.94+.577x=.7x
• 230.94=.123x
• x=1877.6 m
• h=.7x = .7(1877.6)=1314.3 m (approximately, rounding was involved)