Question

At an instant, the length of shadow of a stick is found to be `sqrt(3)` times the length of the stick as shown in the figure below. The Sun’s altitude at that instant is:

Options

• 30°

• 45°

• 60°

• 90°

Answer 1

30°

Explanation:

1. Identify the trigonometric relationship

In a right-angled triangle formed by a stick and its shadow, the Sun’s altitude (θ) is the angle of elevation from the tip of the shadow to the top of the stick.

Let the height of the stick be h.

According to the problem, the length of the shadow is `sqrt(3)h`.

2. Set up the tangent equation

We use the tangent function, which is the ratio of the opposite side to the adjacent side:

`tan(θ) = "Height of stick"/"Length of shadow"`

`tan(θ) = h/(sqrt(3)h)`

3. Simplify and solve for the angle

Canceling out the common factor h gives:

`tan(θ) = 1/(sqrt(3))`

From standard trigonometric tables, we know that:

`tan(30^circ) = 1/sqrt(3)`

Therefore, θ = 30°.