Question

from the top of a tower 100 M high a man observe two car on the opposite sides of the tower and in same same straight line with its base with angle of depression 30 degree and 45 degree find the distance between the cars ​

Answer 1

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Answer 2

Answer:

Step-by-step explanation:

In the triangle ABC,

Let

A be the position of the man

B and C be the position of the two cars

AD be the tower

BD = x -------1

CD = y ------2

Distance between the cars = x + y

In ∆ ADB,

Tan θ = opposite/ adjacent

Tan 30° = AD/ BD

1/√3 = 100/x. (Tan 30° = 1/√3) (BD = x from 1)

x = 100√3

x = 100 x 1.732. (√3 = 1.732)

x = 173.2m

In ∆ ADC,

Tan θ = opposite/ adjacent

Tan 45° = AD / CD

1 = 100/y. (Tan 45° = 1) (CD = y from 2)

y = 100m

Therefore, the distance between the cars = x + y

= 173.2 + 100

= 273.2 m