On a similar concept, a radio station tower was built in two sections A and B. Tower is supported by wires from a point. Distance between the base of the tower and point O is 36 m. From point O, the angle of elevation of the top of section B is 300 and the angle of elevation of the top of section A is 450. What is the height of the section B? (a) 12√3 m
(b) 12√2 m (c) 8√3 m (d) 4√2 m
1
(ii)
What is the height of the section A? (a) 12(2-√2)m
(b) 24(2 - √2) m
(c) 12(3-√3)m
(d) 12(3 - √3) m
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(iii)
What is the length of the wire structure from the point O to the top of section A ? (a) 32√2 m
(b) 24√3 m (c) 28√3 m (d) 36√2 m
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(iv)
What is the length of the wire structure from the point O to the top of section B ? (a) 12√3 m
(b) 24√3 m (c) 28√3 m (d) 16√3 m
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(v)
What is the angle of depression from top of tower to point O ? (a) 300
(b) 450 (c) 150 (d) 750
Answers
Given : Tower is in two sections section B then above that section A
Distance between base of tower and point O is 36 m
From point O , angle of elevation of the top of section B is 30°
From point O , angle of elevation of the top of section A is 45°
To Find : height of the section B
(a) 12√3 m (b) 12√2 m (c) 8√3 m (d) 4√2 m
height of the section A
(a) 12(2-√2)m (b) 24(2 - √2) m (c) 12(3-√3)m (d) 12(3 - √3) m
length of the wire structure from the point O to the top of section A
(a) 32√2 m (b) 24√3 m (c) 28√3 m (d) 36√2 m
length of the wire structure from the point O to the top of section B
(a) 12√3 m (b) 24√3 m (c) 28√3 m (d) 16√3 m
angle of depression from top of tower to point O
(a) 30° (b) 45° (c) 15° (d) 75°
Solution:
height of the section B
Tan 30° = height of the section B / 36
=> 1/√3 = height of the section B / 36
=> height of the section B = 36/√3
=> height of the section B = 12√3
height of the section A
Tan 45° = (height of the section A + height of the section B) / 36
=> 1 = (height of the section A + 12√3) / 36
=> height of the section A = 36 - 12√3
= 12( 3- √3)
length of the wire structure from the point O to the top of section A
=> cos45 = 36/Wire length to the top of section A
=> 1/√2 = 36/Wire length to the top of section A
=> wire length to the top of section A = 36√2
length of the wire structure from the point O to the top of section B
=> cos30 = 36/Wire length to the top of section B
=> √3/2 = 36/Wire length to the top of section B
=> wire length to the top of section A = 24√3
angle of depression from top of tower to point O = 45°
as angle of depression = angle of elevation
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Answer:
What is the height of the section