The horizontal distance H is given.
So the height h1 of the face from the observer's instrument
= H tan(32°)
The height h2 of the top from the observer's instrument
= H tan(35°)
So the height of the face is h2-h1.
I tried to solve this but can't seem to find a procedure to solve this:
To measure the height of Lincoln's caricature on Mt. Rushmore, two sightings 800 feet from the base of the mountain are of Lincoln's face is 32 degrees and the angle of elevation to the top is 35 degrees, what is the height of Lincoln's face?
So far I got tan32= x/800+a and tan35= y/800+a
4 answers
because the sightings were 800 from th base of the mountain shouldn't it be 800 + a ?
When surveyors measure distance, they measure the horizontal distance, even if the distance they actually measured is at an angle.
Recall that tangent(θ) of an angle of elevation is opposite(height)/adjacent(horizontal).
So when the question says that the measures were made 800 ft from the base, it means that the horizontal distance is 800 ft. The vertical distance is therefore 800' tan(θ) where θ is the measured angle.
800' (horizontal) cannot be algebraically added to a (vertical), which is the height of the face. The two measurements are not in the same direction, so cannot be added together numerically.
Draw a diagram and see if you see the light. If not, post again.
Recall that tangent(θ) of an angle of elevation is opposite(height)/adjacent(horizontal).
So when the question says that the measures were made 800 ft from the base, it means that the horizontal distance is 800 ft. The vertical distance is therefore 800' tan(θ) where θ is the measured angle.
800' (horizontal) cannot be algebraically added to a (vertical), which is the height of the face. The two measurements are not in the same direction, so cannot be added together numerically.
Draw a diagram and see if you see the light. If not, post again.
blah blah blah.