Question

A person stands 40 m from a flag pole. With a protractor at eye level, he finds the angle at the top of the flag pole with the horizontal is 25.0 degrees. How high is the flag pole? The distance from his feet to his eyes is 1.8 m.

Answer 1

Answer on Question #48278, Physics, Optics

A person stands $40\mathrm{m}$ from a flag pole. With a protractor at eye level, he finds the angle at the top of the flag pole with the horizontal is 25.0 degrees. How high is the flag pole? The distance from his feet to his eyes is $1.8\mathrm{m}$ .

Solution:

From the right triangle ABC we can find the distance BC (we know the angle and we know the distance $\mathrm{AB} = 40\mathrm{m}$ ):

$$B C = A B \tan 2 5 {}^ {\circ} = 4 0 * \tan 2 5 {}^ {\circ} = 1 8. 6 5 \mathrm {m}$$

The distance OB is equal to the height of the person (which is $1.8 \, \text{m}$ ). Then we can find the whole height of the pole:

$$H e i g h t o f t h e f l a g p o l e = O C = O B + B C = 1. 8 + 1 8. 6 5 = 2 0. 4 5 \mathrm {m}$$

Answer: Height of the flag pole = 20.45 m

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