Class X Session 2023-24 Question 13

 MATH SAMPLE QUESTION PAPER

Class X Session 2023-24

MATHEMATICS STANDARD (Code No.041) 

Question 13

If a pole 6 m high casts a shadow 2 √3m long on the ground, then the Sun’s elevation is

(a) 60° 

(b) 45° 

(c) 30° 

(d) 90°

Explanation :  let's assume 

h as the height of the pole (6 meters)

s as the length of the shadow (2√3 meters)

θ as the Sun's elevation angle

The triangles formed by the pole, its shadow, and the ground are similar. Therefore, the ratio of corresponding sides is equal. In this case, the ratio of the height of the pole to the length of its shadow is the same as the ratio of the height of the observer to the distance from the observer to the tip of the shadow.

\[\therefore \frac{h}{s} \; = \tan\theta\]

\[\Rightarrow \frac{6}{2\sqrt{3}} \; = \tan\theta\]

\[\therefore \sqrt{3} \; = \tan\theta\]

\[\theta\; =\; \sqrt{3}\]

The above question is illustrated in the picture below as well :

Where X = 2√3 and θ = 60°

Guess the Option and comment below  👇