We just started this yesterday in my pre-calculus class so I am still trying to get the hang of it. I have to make a diagram and label it for each word problem and then solve it using trigonometric functions. The problem I am having trouble with is:
How far from the foot of a pole 80 feet high must a 6-foot tall person stand so that the angle of elevation to the top of the pole is 10 degrees?
I understand trigonometric functions, but am having trouble drawing the diagram for this particular problem, which without a diagram to look at is hard to solve. I am not sure if you can draw diagrams or how someone would show me the diagram for this on here but if you know a way please help
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Best Answer
See 1 for a picture with the angle of elevation ($\theta = 10^\circ$) located at the base of the right triangle. The large triangle is determined by the pole, and the known angles of the right triangle. The small triangle is determined by the person's height with the same angles. Set up the equation using similar triangles for $\tan(\theta)$. The distance from the pole to the person is the distance from the pole to the tip of its shadow minus the distance from the person to the tip of the shadow. You should get $\frac{74}{\tan(\theta)} \approx 419.674854652.$