A straight road leads to the foot of the tower of height 48 m. From the top of the tower the angles of depression of two cars standing on the road are 30° and 60° respectively. Find the distance between the two cars. (√3 = 1.73)
Answers
Given data :
- A straight road leads to the foot of the tower of height 48 m.
- From the top of the tower the angles of depression of two cars standing on the road are 30° and 60° respectively.
To find : The distance between the two cars ?
Solution :
We know that, tower is perpendicular to ground.
Now, from figure,
Let, AB be the tower of height 48 m.
According to given :
The tower the angles of depression of two cars standing on the road are 30° and 60° respectively.
We know that alternate angle are equal to each other. hence, first car at point D at an angle 30° and second car at point C at an angle 60°.
Now, to find the distance between the cars. Here, we need to find BC and BD
Now, by trignometric ratio :
⟹ tan ( θ ) = opposite/adjesent
where, θ = 30°
⟹ tan ( 30° ) = AB/BD
⟹ tan ( 30° ) = 48/BD
⟹ 1/√3 = 48/BC
⟹ BD = 48 * √3
⟹ BD = 48 * 1.73
⟹ BD = 83.04 m
Similarly,
⟹ tan ( θ ) = opposite/adjesent
Where, θ = 60°
⟹ tan ( 60° ) = AB/BC
⟹ √3 = 48/BC
⟹ BC = 48/√3
⟹ BC = 48/1.73
⟹ BC = 27.7456 m (approx)
Now,
⟹ Distance between the two cars
= BD - BC
⟹ Distance between the two cars
= 83.04 - 27.7456
⟹ Distance between the two cars
= 55.2944 m
Answer : Hence, the distance between the two cars is 55.2944 m.
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