Question is not clear (Question:549906.0)

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Bony John

· started a discussion

· 1 Months ago

Question is not clear (Question:549906.0)

What if the two pints are on different sides

Question:

P and Q on the same side of a building are two points observed from the top of that building

$ 20\sqrt[]{3}$ m high. If the angles of the points are complementary and PQ = 40 m, then the distance of P from the building is –

Options:

10 m

20 m

15 m

25 m

Solution:

Here, AB is the building of height $20 \sqrt{3}$ m

In ∆ABP,

$t a n (90 ° - θ) = \frac{A B}{P B}$

$c o t θ = \frac{20 \sqrt{3}}{P B}$ .....(i)

In ∆ABQ,

$t a n θ = \frac{A B}{Q B} = \frac{20 \sqrt{3}}{Q P + P B}$

$t a n θ = \frac{20 \sqrt{3}}{40 + P B}$ ......(ii)

From equation (i) and (ii)

$c o t θ \times t a n θ = \frac{20 \sqrt{3}}{P B} \times \frac{20 \sqrt{3}}{40 + P B}$

PB(40 + PB) = 1200

PB² + 40PB – 1200 = 0

PB² + 60PB – 20PB – 1200 = 0

PB(PB + 60) – 20(PB + 60) = 0

(PB – 20) (PB + 60) = 0

So, PB = 20 m

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