NIMCET 2026 Mathematics PYQ — From the top of a viewpoint at a height of 80m, the angles of dep… | Mathem Solvex | Mathem Solvex
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NIMCET 2026 — Mathematics PYQ
NIMCET | Mathematics | 2026
From the top of a viewpoint at a height of 80m, the angles of depression of the top and bottom of a flag standing on the same plane are observed to be 30∘ and 45∘, respectively. Find the height (in metres) of the flag?
Choose the correct answer:
A.
80(1−31)
(Correct Answer)
B.
80(3−1)
C.
403
D.
380
Correct Answer:
80(1−31)
Explanation
To solve this, we can model the situation using a right-angled triangle. Let H=80 m be the height of the viewpoint and h be the height of the flag.
Step 1: Calculate the distance to the flag
Let d be the distance between the viewpoint and the base of the flag. Since the angle of depression to the bottom of the flag is 45∘, the angle of elevation from the bottom to the top of the viewpoint is also 45∘.
tan(45∘)=Distance dHeight of viewpoint
1=d80
d=80 m
Step 2: Calculate the height of the flag
The angle of depression to the top of the flag is 30∘, which means the angle of elevation from the top of the flag to the viewpoint is 30∘. The height of the viewpoint above the top of the flag is (80−h).
tan(30∘)=Distance dVertical distance
31=8080−h
Now, solve for h:
80−h=380
h=80−380
Factoring out 80:
h=80(1−31)
Thus, the height of the flag is 80(1−31) meters.
Explanation
To solve this, we can model the situation using a right-angled triangle. Let H=80 m be the height of the viewpoint and h be the height of the flag.
Step 1: Calculate the distance to the flag
Let d be the distance between the viewpoint and the base of the flag. Since the angle of depression to the bottom of the flag is 45∘, the angle of elevation from the bottom to the top of the viewpoint is also 45∘.
tan(45∘)=Distance dHeight of viewpoint
1=d80
d=80 m
Step 2: Calculate the height of the flag
The angle of depression to the top of the flag is 30∘, which means the angle of elevation from the top of the flag to the viewpoint is 30∘. The height of the viewpoint above the top of the flag is (80−h).
tan(30∘)=Distance dVertical distance
31=8080−h
Now, solve for h:
80−h=380
h=80−380
Factoring out 80:
h=80(1−31)
Thus, the height of the flag is 80(1−31) meters.
