Question

A bird is perched at the top of a tree at an angle of elevation of 60° from a point a on the ground. If the bird descends half way down the vertical height of the tree, find the new angle of elevation from a to the new position of the bird perched.

Answer 1

Answer:

40.9°

Step-by-step explanation:

tan 60 = h/l = √3

tan∝ = h/2l = √3/2

∝ = tan∧-1 (√3/2) = 40.9°

Answer 2

The new angel of elevation form the new position of the bird perched is $\theta=\tan^{-1}\frac{\sqrt{3}}{2}$.

Step-by-step explanation:

Consider the provided information.

Let AB is x and BC is the height of tree = h.

D represents the Mid point which is half way down,

It is given that ∠CAB = 60° and we need to find the value of ∠DAB.

In ΔABC

$\tan60^0=\frac{BC}{AB}$

$\sqrt{3}=\frac{h}{x}$

$h=\sqrt{3}x$

In ΔDBA

$\tan\theta=\frac{DB}{AB}$

$\tan\theta=\frac{\frac{h}{2}}{x}$

$\tan\theta=\frac{h}{2x}$

Substitute the value of h in $\tan\theta=\frac{h}{2x}$

$\tan\theta=\frac{\sqrt{3}x}{2x}$

$\tan\theta=\frac{\sqrt{3}}{2}$

$\theta=\tan^{-1}\frac{\sqrt{3}}{2}$

The new angel of elevation form the new position of the bird perched is $\theta=\tan^{-1}\frac{\sqrt{3}}{2}$.

#Learn more

The angle of depression of the top of a tree of height 30ft is 60• from the top of another tree. find the height of other tree​

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