Question

From the top of a building h metre high, the angle of depression of an object on the ground has measure θ. The distance (in metres) of the object from the foot of the building is.......,select a proper option (a), (b), (c) or (d) from given options so that the statement becomes correct.
(a) h sinθ
(b) h tanθ
(c) h cotθ
(d) h cosθ

Answer 1

We know, height of the building h meter

Let the object distance is x meter

angle of depression also known to us which is θ.

Now as shown in the figure,

cotθ = $\frac{base}{perpendicular}$

= $\frac{x}{h}$

Hence, x = hcotθ

option c is correct.

distance of object from building is hcotθ

Answer 2

Dear student,

Answer: Distance of object from the building's foot is h cot θ.option c is correct.

Solution:

As we know that height of building is taking as perpendicular in the triangle, and distance of object is taking as base.

Now take the trigonometric ratio which include both perpendicular and base

i.e.

tan θ = $\frac{perpendicular}{Base}$

Since according to question height of building is h meters

tan θ = $\frac{h}{Base}$

Base ( tan θ) = h

Base = h/tan θ

Base = h cot θ

So,distance of object from the building's foot,is given by h cot θ.

hope it helps you.