A flagpole casts a shadow 17 m long. The angle of elevation from the tip of the shadow to the top of the flagpole is 58 . How high is the flagpole to the nearest decimal?
tan = opposite/adjacent
tan 58 = h/17
multiply 17 times the tan of 58 to find h.
20 ft
To find the height of the flagpole, we can use trigonometry.
Let's assume the height of the flagpole is h.
We have a right triangle formed by the flagpole, its shadow, and the line of sight from the tip of the shadow to the top of the flagpole.
The angle of elevation is 58°, which means the angle between the ground and the line of sight from the tip of the shadow to the top of the flagpole is 90° - 58° = 32°.
In a right triangle, the tangent of an angle is defined as the opposite side divided by the adjacent side.
In this case, the opposite side is the height of the flagpole (h) and the adjacent side is the length of the shadow (17 m).
So, we have tan(32°) = h / 17.
To find h, we can rearrange the formula:
h = 17 * tan(32°).
Using a calculator, compute tan(32°) and multiply it by 17.
h ≈ 17 * 0.62487 ≈ 10.62.
Therefore, the height of the flagpole is approximately 10.62 meters to the nearest decimal.