Question

From two points A and B on the same side of a building, the angles of elevation of the top of the buildings are 30 and 60° respectively. If the height of the building is 10 m. find the distance between A and B correct to two decimal places.
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Answer 1

Answer: distance = 11.54 m

Step-by-step explanation:

Let the height of the building be HH’ = 10 m with H at the foot of the building and H’ at the top of the building

Let the distance of point A to the foot of the building = AH

Let the distance of point B to the foot of the building = BH

Angle of elevation from A to H’ = 30°

Angle of elevation from B to H’ = 60°

Tan30° = 1/√3 = HH’/AH

=> AH = HH’ * √3 = 10√3

Tan60° = √3/1 = HH’/BH

=>BH = HH’ / √3 = 10/√3

Distance between the points A and B = AH - BH ( B is closer to the foot of the building than A since it subtend a larger angle of elevation)

Distance = 10√3 - 10/√3 = 10 * ( √3 - 1/√3) = 10 * (3-1/√3) = (10*2)/√3

=> distance = 20/√3 = 20*√3/ 3 = (20 * 1.732) / 3

=> distance = 34.64/3

=> distance = 11.54 m

Please brainlist my answer, if helpful!