Question

The angle of depression from the top of a building to a point

on the ground is 45 degrees.
How far is the point on the ground from the top of the building
if the building is 280 m high?
Round your answer to the nearest whole number

Answer 1

The distance between point on the ground from the top of the building is 396 meter, if the building is 280 m high and The angle of depression from the top of a building to a point on the ground is 45 degrees.

Explanation:

The given is,

The angle of depression from the top of a building to a point on the ground is 45 degrees.

Height of the building is 280 meter.

Step: 1

Given diagram is a right angled diagram,

For right angle triangle,

90° = 45° + 45°

= 90°

Trignometric ratio,

sin ∅ =
`(Opp)/(Hyp)`....................(1)

For the above ratio take the bottom angle, that is angle of depression from the top of a building to a point on the ground is 45 degrees.

Where, Opp side = 280 meters

Hyp side = x

∅ = 45°

Equation (1) becomes,

sin 45° =
`(280)/(x)`

0.70710678 =
`(280)/(x)`

x =
`(280)/(0.70710678)`

x = 395.979

Distance between point on the ground from the top of the building, x ≅ 396 meter

Trignometric ratio,

cos ∅ =
`(Adj)/(Hyp)`

Cos 45 =
`(Adj)/(396)`

Adj = (0.70710678)(396)

Bottom length, Adj = 280 meter

Result:

The distance between point on the ground from the top of the building is 396 meter.