Answer :
Final answer:
To find the height of the building, the formula h = tan(23°) * 186 feet is used. The calculated height, using the tangent of the given angle and the known distance, is approximately 78.3 feet.
Explanation:
To calculate the height of the building, we will use trigonometry, specifically the tangent function, which is the ratio of the opposite side to the adjacent side in a right-angled triangle. The angle we have been given is 23° (the angle from the ground to the top of the building), and the distance from the observer to the base of the building is 186 feet. We can represent the situation as a right-angled triangle where the tangent of the angle will be the height of the building divided by the distance from the building.
The formula to calculate the height (h) of the building is:
tan(theta) = opposite/adjacent
where theta is the angle of elevation (23°), the opposite is the height of the building, and the adjacent is the distance from the observer to the building (186 feet).
To find the height of the building, we rearrange the formula to: h = tan(theta) * adjacent
Plugging in our values, we get: h = tan(23°) * 186 feet
Using a calculator, we find that: h = tan(23°) * 186 ≈ 78.3 feet (rounded to one decimal place)
Therefore, the approximate height of the building is 78.3 feet.
9514 1404 393
Answer:
about 79 ft
Step-by-step explanation:
The relevant trig relation is ...
Tan = Opposite/Adjacent
In this scenario, the angle is 23°, the adjacent side is the distance to the building, and the opposite side is the building height. Then we have ...
height = tan(23°)·(186 ft) ≈ 78.95 ft ≈ 79 ft
