Question

of the top of a tower from two points distant s and t from its foot are complementary. Prove that the height of the tower is √st.​

Answer 1

[HeY Mate]

Answer:

Question:

The angle of elevation of the top of a tower from two points distant s and t from its foot are complementary. Prove that the height of the tower is √st.

Solution:

Let BC = s; PC = t

Let the height of the tower be AB = h.

∠ABC = θ and ∠APC = 90° – θ

(∵ the angle of elevation of the top of the tower from two points P and B are complementary)

In triangle ABC,

tan θ = AC/BC = h/s ………..(i)

In triangle APC,

tan (90° – θ) = AC/PC = h/t

cot θ = h/t ………..(ii)

Multiplying (i) and (ii),

tan θ × cot θ = (h/s) × (h/t)

1 = h2/st

h2 = st

h = √st

Hence, the height of the tower is √st.

I Hope It Helps You✌️