SOLUTION: Two, surveyors, Mark and Dan, need to determine the height of a steep cliff. They stand 50m apart, where they each have a clear view of the cliff and each other. Mark measures an a

Question 1065291: Two, surveyors, Mark and Dan, need to determine the height of a steep cliff. They stand 50m apart, where they each have a clear view of the cliff and each other. Mark measures an angle of elevation of 61� from the base of the cliff to its highest point. From where Mark is standing he also measures the angle between Dan and the base of the cliff at 72�. Dan measures the angle between Mark and the base of the cliff at 38�. How tall is the cliff?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Two, surveyors, Mark and Dan, need to determine the height of a steep cliff. They stand 50m apart, where they each have a clear view of the cliff and each other. Mark measures an angle of elevation of 61� from the base of the cliff to its highest point. From where Mark is standing he also measures the angle between Dan and the base of the cliff at 72�. Dan measures the angle between Mark and the base of the cliff at 38�. How tall is the cliff?
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Sketch the figure::
You have a triangle on the ground with angles 72,38,180-(72+38) = 70
The side opposite the 70 degree angle is 50 meters.
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Let m be the side opposite the 38 deg angle
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Use the Law of Sines::
m/sin(38) = 50/sin(70)
m = 32.76 meters
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Find the height of the hill.
You have a right triangle with height = h , hypotenuse = 32.76 meters,
and base angle = 61 degrees
sin(61) = h/32.76
Ans:: height = 28.65 meters
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Cheers,
Stan H.
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