Question

two persons are standing on the same side of a tall building notice the angle of elevation of the top of the building to be 30 and 60 respectively If 5he height of the building is 72 m find the distance between the two persons

Answer 1

▶ Question :- 

→ Two persons on same side of tall building notice angle of elevation of top of building to be 30° and 60°. If height of building is 72m, find distance between two persons .


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→ Let AB be the height of the building = 72 m .

→ And, suppose two person standing at point C and D making an angle of elevation to the top of the building is 60° and 30° respectively.

→ Let the distance between two person CD be x m.

→ And, CB = y m.


▶ Now, 

In right ∆ABC, 

$\begin{lgathered}\sf \because \tan 60 \degree = \frac{AB}{BC}. \\ \\ \sf \implies \sqrt{3} = \frac{72}{y} . \\ \\ \sf \implies y = \frac{72}{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } . \\ \\ \sf \implies y = \frac{72 \sqrt{3} }{3} . \\ \\ \sf \therefore y = 24 \sqrt{3} m.\end{lgathered}$

And, 

In right ∆ABD 

$\begin{lgathered}\sf \because \tan 30 \degree = \frac{AB}{BD} . \\ \\ \sf \implies \frac{1}{ \sqrt{3} } = \frac{72}{x + y} . \\ \\ \sf \implies \frac{1}{ \sqrt{3} } = \frac{72}{x + 24 \sqrt{3} } . \\ \\ \sf \implies x + 24 \sqrt{3} = 72 \sqrt{3} . \\ \\ \sf \implies x = 72 \sqrt{3} - 24 \sqrt{3} . \\ \\ \boxed{ \pink{ \sf \therefore x = 48 \sqrt{3} m.}} \\ \\ or \\ \\ \boxed{ \pink{ \sf \therefore x = 83.04 m.}}\end{lgathered}$


✔✔ Hence, the distance between two person is 83.04 m ✅✅ .


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Answer 2

Solution:

Let the height of building be (PQ) and distance from buildings are a(R) and b(S) meter.

In Δ PQR ,

Tan 30° = PQ/QR

⇒ √3 = 72/a

⇒ a = 72/√3

⇒ a = 24√3

Again ,

In Δ PQS ,

Tan 60 °= PQ/QS

⇒ 1/√3 = 72/b

⇒ b = 72√3

Now,

Total distance:

QS = a - b

QS = 24√3 - 72√3

⇒ QS = 48√3

⇒ QS = 83.04 m

Hence, The required distance between the two persons is 83.04 metre.