NIMCET 2014 Mathematics PYQ — From three collinear points , and on a level ground, which are on… | Mathem Solvex | Mathem Solvex
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NIMCET 2014 — Mathematics PYQ
NIMCET | Mathematics | 2014
From three collinear points A, B and C on a level ground, which are on the same side of a tower, the angles of elevation of the top of the tower are 30∘, 45∘ and 60∘ respectively. If BC=60 m, then AB is:
Choose the correct answer:
A.
153 m
B.
303 m
C.
453 m
D.
603 m
(Correct Answer)
Correct Answer:
603 m
Explanation
Solution
1. Geometric Setup:
Let QP be the tower of height h standing on point P. The points C,B,A are on the ground such that the angles of elevation to the top Q are 60∘,45∘, and 30∘ respectively.
2. Expressing Distances in terms of Tower Height (QP):
Using the trigonometric ratio tanθ=BasePerpendicular:
In △QPA: AP=tan30∘QP=3QP
In △QPB: BP=tan45∘QP=QP (since tan45∘=1)
In △QPC: CP=tan60∘QP=3QP
3. Finding the Height of the Tower (QP):
It is given that BC=60 m. From the diagram:
BP−CP=60
QP−3QP=60
QP(33−1)=60
QP=3−1603…(1)
4. Calculating Distance AB:
We need to find AB, which is the distance between points A and B:
AB=AP−BP
AB=3QP−QP
AB=QP(3−1)
Substitute the value of QP from equation (1):
AB=(3−1603)⋅(3−1)
AB=603 m
Correct Option: 4 (603 m)
Explanation
Solution
1. Geometric Setup:
Let QP be the tower of height h standing on point P. The points C,B,A are on the ground such that the angles of elevation to the top Q are 60∘,45∘, and 30∘ respectively.
2. Expressing Distances in terms of Tower Height (QP):
Using the trigonometric ratio tanθ=BasePerpendicular:
In △QPA: AP=tan30∘QP=3QP
In △QPB: BP=tan45∘QP=QP (since tan45∘=1)
In △QPC: CP=tan60∘QP=3QP
3. Finding the Height of the Tower (QP):
It is given that BC=60 m. From the diagram:
BP−CP=60
QP−3QP=60
QP(33−1)=60
QP=3−1603…(1)
4. Calculating Distance AB:
We need to find AB, which is the distance between points A and B:
