on a straight line passing through the foot of a tower,two points C and D are at a distances of 4m and 16m from the foot respectively,If the angle of elevation from C and D of the top of a tower are complementary,then find the height of a tower.
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Angles are complementary therefore one will be 'theta' and the other will be '90-theta'
Tan theta = AB/16 where AB is the height of tower------1
Tan (90-theta)= AB/4------2
Tan (90-theta)= cot theta
Multiply 1 and 2
Tan theta * cot theta = AB/ 16 * AB/4
1 = AB^2/64
64= AB^2
AB=8
Angles are complementary therefore one will be 'theta' and the other will be '90-theta'
Tan theta = AB/16 where AB is the height of tower------1
Tan (90-theta)= AB/4------2
Tan (90-theta)= cot theta
Multiply 1 and 2
Tan theta * cot theta = AB/ 16 * AB/4
1 = AB^2/64
64= AB^2
AB=8
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