Question

The angle of elevation of the top of building 30m high from the foot of another building in the same plane is 60(degree)and also angle of elevation of top of second building from foot of first building is 30(degree) then distance between 2 buildings __________. ​

Answer 1

Answer:

Distance between the buildings = 10√3 m

Step-by-step explanation:

Given:

• Height of the second building = 30 m
• Angle of elevation to the second building = 60°
• Angle of elevation to the first building = 30°

To Find:

• The distance between the two buildings

Solution:

Let the height of the first building be AB

Let the height of the second building be DC = 30 m

Let the distance between the buildings be BC

Here we have to find the distance between the buildings.

Now consider Δ DCB

tan 60 = DC/BC

tan 60 = 30/BC

√3 = 30/BC

Cross multiplying,

BC√3 = 30

BC = 30/√3

Rationalising the denominator,

BC = 30√3/3

BC = 10√3 m

Hence the distance between the two building is 10√3 m.

Notes:

Sin A = opposite/hypotenuse

Cos A = adjacent/hypotenuse

tan A = opposite/adjacent

Answer 2

Step-by-step explanation:

Given :

• The angle of elevation of the top of building 30m high from the foot of another building in.

• the same plane is 60° and also angle of elevation of top of second building from foot of first building is 30°

To Find :

• then distance between 2 buildings __________. 

Solution :

Concept :

Trigonometry Functions Formulas

• In a right-angled triangle, we have 3 sides namely – Hypotenuse, Opposite side (Perpendicular) and Adjacent side (Height). The longest side is known as the hypotenuse, the side opposite to the angle is perpendicular and the side where both hypotenuse and opposite side rests is the adjacent side.

In DCB,

➥ Tan 60° = P / B

• Tan 60° = √3

➥ √3 = 30 / BC

➥ √3BC = 30

➥ BC = 30 / √3

➥ BC = 10√3

By using a right-angled triangle as a reference, the trigonometric functions or identities are derived:

• sin θ = Opposite Side/Hypotenuse

• sec θ = Hypotenuse/Adjacent Side

• cos θ = Adjacent Side/Hypotenuse

• tan θ = Opposite Side/Adjacent Side

• cosec θ = Hypotenuse/Opposite Side

• cot θ = Adjacent Side/Opposite Side

In ABC

➥ Tan30 = P / B

➥ 1 / √3 = AB / 10√3

➥ √3AB = 10√3

➥ AB = 10√3 / √3

➥ AB = 10

• then distance between 2 buildings is 10 Cm