Question

0. When the length of the shadow of a pillar is equal to its height, the elevation at source of sight is
at source of sight is :
(a) 30 degree (b) 45 degree
(c) 60 degree (d) 90 degree​

Answer 1

Answer:

(b) 45 degree

Step-by-step explanation:

HOPE IT HELPS....

Answer 2

Answer:

Option (b) 45°.

Step-by-step explanation:

(Refer to the figure attached below)

AB $\longrightarrow$ Pillar.

BC $\longrightarrow$ Shadow.

θ $\longrightarrow$ Angle of elevation.

ATQ,

The height of pillar, and the length of the shadow are equal to each other.

$\Longrightarrow \sf Height \ of \ Pillar = Length \ of \ shadow\\ \\ \Longrightarrow \sf AB = BC\\ \\ \Longrightarrow \sf \dfrac{AB}{BC} = 1 \ \ \longmapsto \ Eq(1)$

In ΔABC,

∠ABC = 90°

$\Longrightarrow \ \sf tan\theta = \dfrac{Opposite \ Side}{Adjacent \ Side}\\ \\ \\\Longrightarrow \ \sf tan\theta = \dfrac{AB}{BC}\\ \\ \\\sf Applying \ Eq(1) \ above \ we \ get,\\ \\ \\\Longrightarrow \ \sf tan\theta = 1$

But tan45° = 1

$\Longrightarrow \sf \theta = 45^\circ$

Therefore, the angle of elevation of the pillar from the source of sight is 45°, making the answer Option(b) 45°.

Alternative method:

In ΔABC,

AB = BC

∴ ∠1 = ∠2

(Angles opposite to equal sides are equal)

By ASP of a triangle,

∠1 + ∠2 + ∠ABC = 180°

We've proved that ∠1 = ∠2, therefore,

∠1 + ∠1 + ∠ABC = 180°

2∠1 + 90° = 180°

2∠1 = 180° - 90°

2∠1 = 90°

∠1 = 90°/2

∠1 = 45°

Therefore the angle of elevation is 45°.