To find the height of the building, we can use the tangent of the angle of elevation. The formula relating the height (h) of the building to the angle of elevation (\(\theta\)) and the distance from the object (d) is:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]
In this case, the opposite side is the height of the building minus the height of Jack's eyes (h - 5 feet), and the adjacent side is the distance from Jack to the building (400 feet).
Given:
- Angle of elevation \(\theta = 67°\)
- Distance from the building (d) = 400 feet
- Height of Jack's eyes = 5 feet
We can set up the equation:
\[ \tan(67°) = \frac{h - 5}{400} \]
Now we can solve for \(h\):
- Find \(\tan(67°)\):
Using a calculator, \(\tan(67°) \approx 2.35585\).
- Substitute into the equation:
\[ 2.35585 = \frac{h - 5}{400} \]
- Multiply both sides by 400:
\[ h - 5 = 2.35585 \times 400 \]
Calculating:
\[ h - 5 = 942.34 \]
- Add 5 to both sides:
\[ h = 942.34 + 5 \]
\[ h = 947.34 \]
Thus, the height of the building is approximately 947 feet.
The answer is:
D. 947 ft