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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