Two spotlights, P and Q are mounted on a vertical pole AB as shown.
Light beams from P and Q shine to two points on the ground,
H and K, respectively. Given that PQ = 16 m, KB = 16 m,
PH = 35 m and QK = 20 m, Find:
(i)BQ, the height above the ground at which the spotlight Q is mounted
(ii)HK, the distance between the projections of the light beams
Answers
Given : Two spotlights, P and Q are mounted on a vertical pole AB as shown. Light beams from P and Q shine to two points on the ground, PQ = 16 m , KB = 16 m PH = 35 m QK = 20 m
To Find : BQ, the height above the ground at which the spotlight Q is mounted & HK, the distance between the projections of the light beams
Solution:
BK = 16 m
BQ = ?
KQ = 20 m
KQ² = BK² + BQ²
=> 20² = 16² + BQ²
=> 400 = 256 + BQ²
=> BQ² = 144
=> BQ = 12 m
the height above the ground at which the spotlight Q is mounted = 12 m
PQ = 16
BP = BQ + PQ
=> BP = 12 + 16
=> BP = 28
HP = 35
BH² = HP² - BP²
=> BH² = 35² - 28²
=> BH² = (35 + 28)(35 - 28)
=> BH² = 63 * 7
=> BH² = 3 * 3 * 7 * 7
=> BH = 3 * 7
=> BH = 21
HK = BH - BK
21 - 16 = 5
=> HK = 5 m
the distance between the projections of the light beams = 5 m
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This question is from Triangles chapter of class 10.
It is based on Pythagoras Theorem and is important for students appearing in board exams 2021.
Answer:
i) 12m
ii) 5m
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