What Is the Height of the Pole in This Trigonometry Problem?

[mathdad]

A little review of trigonometry.

A man 1.5m tall is standing 4m away from a pole. If the angle of elevation of the top of the pole is 30 degree,
calculate the height of the pole.

My set up is here.

Let x = height of pole

1.5 + tan30 = x/4

4*tan(30) = x + 4(1.5)

Correct?

 

[MarkFL]

I would let P (in m) be the height of the pole, and let x be the difference between the height of the pole and the height of the man, i.e.:

x = P - 1.5

or:

P = x + 1.5

Constructing a right triangle, we obtain:

tan(30°) = x/4 which implies x = 4 tan(30°)

And so we have:

P = 4 tan(30°) + 1.5

$$P=\frac{4}{\sqrt{3}}+\frac{3}{2}=\frac{8+3\sqrt{3}}{2\sqrt{3}}=\frac{9+8\sqrt{3}}{6}\approx3.809401076758503$$

 

[mathdad]

How about tan(30) = 4/(x - 1.5)?

 

[MarkFL]

How about tan(30) = 4/(x - 1.5)?

You would want:

tan(30°) = (x - 1.5)/4

The tangent function represents the ratio of opposite/adjacent in a right-triangle. :D

 

[mathdad]

You would want:

tan(30°) = (x - 1.5)/4

The tangent function represents the ratio of opposite/adjacent in a right-triangle. :D

How about cot(30) = 4/(x - 1.5)?

 

[MarkFL]

How about cot(30) = 4/(x - 1.5)?

Yes, that would be correct. :D

 

[mathdad]

Cool. Now back to precalculus. Check out my absolute value questions.