the angle of elevation of the top of a vertical mast from a point on level ground 240 m from its foot is 31.5°.How high is the mast
To find the height of the mast, we can use trigonometry.
Let's denote the height of the mast as h.
The given information can be represented by the following diagram:
A - Mast's top
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h | \
| \
| \
| \
| \
| \
| \
| \
| \
| \
O-------------B
240 m
In this right triangle OAB, we know the angle OAB is 31.5° and the side OA is the height of the mast (h), and side AB is the distance from the foot of the mast to the observer (240 m).
Using trigonometry, we can write the following equation:
tan(31.5°) = h / 240
To solve for h, we can rearrange the equation to isolate h:
h = 240 * tan(31.5°)
Using a calculator, we find:
h ≈ 240 * 0.6323
h ≈ 151.8
Therefore, the height of the mast is approximately 151.8 meters.