20. The angle of elevation of a building from two points P and Q on the level ground on the
same side of the building are 36 and 54° respectively. If the distance of the points P and Q
from the base of the building are 10m and 20m respectively, find the height of the building,
(Take root 2 = 1.414)
Ans. 14.14 m
Answers
the height of the building, = 14.14 m
Step-by-step explanation:
height of the building = H
Tan 36 = H/20
=> Tan ( 45 - 9) = (Tan 45 - Tan 9)/(1 + Tan45Tan9)
= (1 - Tan 9)/(1 + Tan9) = H/20
Tan 54 = H/10
=> Tan ( 45 + 9) = (Tan 45 + Tan 9)/(1 - Tan45Tan9)
= (1 + Tan 9)/(1 - Tan9) = H/10
Multiplying both
(1 - Tan 9)/(1 + Tan9) * (1 + Tan 9)/(1 - Tan9) = (H/20)(H/10)
=> 1 = H²/200
=> H² = 200
=> H = 10√2
H = 10 * 1.414
=> H = 14.14 m
the height of the building, = 14.14 m
(Question data is not consisntent as given values not satisfying trignometric values) Tan36 ≠ 14.14/20 its 35.26° & Tan54 ≠ 14.14/10 its 54.74
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