Q) A kite is flying at a height of 60 m above the ground level. Ravi, standing at the roof of the house is holding the string straight and observes the angle of elevation of kite as 30 ⁰ . From the bottom of the same building, the angle of elevation of kite is 45 ⁰. Find the length of the string and height of roof from the ground. (Use √3 = 1.73).

(Q 32 – 30/4/2 – CBSE 2026 Question Paper)

Ans:

Step 1: Let’s make a diagram for our better understanding of the question:

Here, CD is the building of height H, and A is the kite at height of 60 m from point B on ground.

Given that ∠ ADE = 30 ⁰ and ∠ACB is 45 ⁰

Let the length of the string be L m and height of roof from the ground be H m.

Step 2: In Δ ACB, tan 45 ⁰ =

∴ 1 =

∴ BC = 60 m

Step 3: In rectangle CDEB, DE = BC = 60 m

In Δ ADE, cos 30 ⁰ =

∴

∴ L =

=

= 40√3 = 40 x 1.73 = 69.2 m

Step 4: In rectangle CDEB, CD = BE = H

∴ AE = AB – BE = 60 – H

In Δ ADE, sin 30 ⁰ =

∴

∴ 60 – H =

= 20√3 = 20 x 1.73 = 34.6 m

∴ H = 60 – 34.6 = 25.4 m

Therefore, the length of the string is 69.2 m and height of roof from the ground is 25.4 m

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