Question

A vertical flag staff stand on the edge of the vertical building. A surveyor 148m from the the building measure the angle of elevation of the top and bottom of flag staff as 52degrees and 47degrees. Calculate the height of the flag staff

Answer 1

Answer:

Height of the flagstaff if 30.78 m.

Step-by-step explanation:

1. The bottom of the flagstaff denotes the building height whereas the top of the staff denotes the height of the building plus the height of the flagstaff.
2. Let the height of the building be 'b' and that of the flagstaff be 'f'. Also let 'Ф' denote the angle of elevation.
3. We know that, in trigonometry, tanФ = $\frac{opposite side}{adjacent side}$.
4. The length of the adjacent side in both cases is 148 m as given in the question.
5. Taking angle of elevation for bottom of the flag staff i.e., Ф = 47° we get tan(47°) = $\frac{b}{148}$.
6. Therefore, b = tan(47°) * 148
7. Therefore, b = 1.072 * 148
8. Therefore, b = 158.66 m
9. Similarly taking angle of elevation for top of the flag staff i.e., Ф = 52°, we get tan(52°) = $\frac{(b + f)}{148}$.
10. Therefore, (b + f) = tan(52°) * 148
11. Therefore, (b + f) = 1.28 * 148
12. Therefore, (b + f) = 189.44 m
13. Now if we subtract the height of the building from this height, we will get the height of the flagstaff.
14. Therefore, f = (b + f) - b
15. Therefore, f = 189.44 - 158.66
16. Therefore, f = 30.78 m
17. Hence, we have found that the height of the flagstaff is 30.78 m.