Question

From a top of a building 100m high the angle of depression of two objects, on the

same side, are observed to be 45 degrees and 60 degrees . Find the distance between the objects.​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Concept

The study of correlations between triangles' side lengths and angles is known as trigonometry. The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research.

Given

From a top of a building 100m high the angle of depression of two objects, on the same side, are observed to be 45 degrees and 60 degrees is given

Find

We have to find distance between two buildings

Solution

The steps are as follow:

• From the given statement we can draw a figure which is as below
• AB and CD represent two buildings
• In ΔAEC,

tan45 = CE/AE

1 = (100-h)/x

x = 100 - h --------------------------(1)

Where,

h = Ab

x = Distance between two buildings = AE

• In ΔBDC,

tan60 = CD/BD

√3 = 100/x

x = 100/√3 --------------------------(2)

• Comparing equation (1) and (2), we get

100 - h = 100/√3

100√3 - √3h = 100

173 - 1.73h = 100

1.73h = 173 -100

h = 42.19 m

• Putting value of h in equation (1)

x = 100 - h

x = 100 - 42.19

x = 57.80 m

Hence the distance between two buildings will be 57.80 m

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