Isabella and Alice are standing some distance apart on the same side of a building 50 meters tall. From where Isabella stands, the angle of elevation of the top of the building is 30. From where Alice stands, the angle is 60. What is the distance between Isabella and Alice to the nearest tenth of a meter?

57.7 m

Step-by-step explanation:

Since the distance between Isabella, the building and the angle form a right angled triangle with the height of the building = h = 50 m as the opposite side and x = distance between Isabella and the building = adjacent side and Ф = angle of elevation of the top of the building from Isabella = 30°.

So, from trigonometric ratios,

tanФ = h/x

and x = h/tanФ

= 50 m/tan30°

= 50/0.5774

= 86.6 m

Also, the distance between Alice, the building and the angle form a right angled triangle with the height of the building = h = 50 m as the opposite side and x' = distance between Alice and the building = adjacent side and Ф' = angle of elevation of the top of the building from Alice = 60°.

So, from trigonometric ratios,

tanФ' = h/x'

and x' = h/tanФ'

= 50 m/tan60°

= 50/1.7321

= 28.87 m

So, the distance between Isabella and Alice, x" = x - x'

= 86.6 m - 28.87 m

= 57.73 m

≅ 57.7 m