From a point 450 ft from the base of a building, the angles of elevation of the top and bottom of a flagpole on top of the building have measures 60° and 55°. How do you find the height of the flagpole to two significant digits?

Question

Zoe Austin · Accepted Answer

I found #~~135"ft"# rounding the tangents or #136.76"ft"# using the complete values.

I used the trigonometric Tangent to find the value.

Charles Autterson · Answer

undefined To find the height of the flagpole, you can use trigonometry. First, calculate the distance from the point to the base of the flagpole using the tangent function. Then, subtract the height of the building from this distance to get the height of the flagpole. Here's the calculation:

1. Calculate the distance from the point to the base of the flagpole:
$$ \tan(60°) = \frac{{\text{{height of building}}}}{{\text{{distance to base of flagpole}}}} $$
$$ \text{{Distance to base of flagpole}} = \frac{{\text{{height of building}}}}{{\tan(60°)}} $$

2. Subtract the height of the building from the distance to the base of the flagpole to find the height of the flagpole:
$$ \text{{Height of flagpole}} = \text{{Distance to base of flagpole}} - \text{{height of building}} $$

Substitute the given values and calculate to find the height of the flagpole to two significant digits.