Question

Hari standing on the top of a building is the top of the tower of the angle of elevation of 50 degree and the foot of Tower at the angle of depression of 20 degree Hari is 1.6 metre and the height of the building on which he is standing is 9.2 a draw a sketch according to the given information be draw in the tower how how much far is tower from the building C calculate the height of the tower​

Answer 1

$\textsf{\underline{\large{Correct\:Question:-}}}$

Hari, standing on the top of a building, sees the top of a tower at an angle of elevation of 50° and the foot of the tower at an angle of depression of 20°. Height of Hari is 1.6 metre and height of the building on which he is standing is 9.2 metre.

Draw a rough sketch according to the given information.  How much far is the tower from the building?

Calculate the height of the tower.

$\huge\mathfrak{\underline{Solution:-}}$

For diagram, refer the given attachment.

According to this, Height of building ( SU ) =9.2 m. Hari is standint at point S, his height is 1.6 m.

→ It is given that the angle of elevation of 50° and the foot of Tower at the angle of depression of 20°. Now,

To find the distance of the tower from the building, we have to find PV,

In this,

• QR = ST
• ST = UV
• In short, QR = ST = UV.

Now,

In Δ QRV,

$\sf \dfrac{RV}{QR} = tan\:20 \\\\ \implies QR =\dfrac {RV}{tan\:20} \\\\ \implies QR = \dfrac{RT + TV}{0.36}$

$\implies {QR} = \dfrac{1.6+9.2}{0.36}$

$\implies QR =\dfrac{10.8}{0.36} \\\\ \implies QR = 30$

Hence, Tower is 30 m far from the building.

Finally,

→ Height of the tower :

PV is the height of the given tower.

→ PV = PR + RT + TV

$\sf {PV} = {PR} + {1.6\:m}+ {9.2\:m} \\\\ \implies {PV} = {PR} + {10.8}$

Now, to find PR, In ΔQPR, PR is height.

$\sf \dfrac{PR}{QR} = \:tan\:50 \\\\ \implies \dfrac{PR}{30} = 1.19 \\\\ \implies {PR} = 1.19 × 30 \\\\ \implies {PR} = 35.7\:m$

Finally,

→ Height of the tower

= 10.8 m  + 35.7 m

= 46.5 m

Hence,

Height of the tower is 46.5 m

$\rule{200}2$

Answer 2

$\huge{\underline{\underline{\red{\mathfrak{Correct \: Question}}}}}$

Hari, standing on the top of a building, sees the top of a tower at an angle of elevation of 50° and the foot of the tower at an angle of depression of 20°. Height of Hari is 1.6 metre and height of the building on which he is standing is 9.2 metre.

Draw a rough sketch according to the given information. How much far is the tower from the building?

Calculate the height of the tower?

$\rule{200}{2}$

$\huge{\underline{\underline{\red{\mathfrak{Answer :}}}}}$

(1).

We know that,

$\implies{\boxed{\blue{\sf{tan \theta = \frac{Perpendicular}{Base}}}}}$

Here, θ = 20°

Perpendicular = 10.8 m

Base = x

Now, (Putting Values)

$\sf{0.36 = \frac{10.8}{x} } \\ \\ \sf{x = \frac{10.8}{3.6} } \\ \\ \\ \boxed{ \green{\sf{x = cd = 30 \: m}}}$

_______________________

(2).

$\implies{\boxed{\pink{\sf{tan \theta = \frac{Perpendicular}{Base}}}}}$

Where,

θ = 50°

Perpendicular = HF

Base = 30

Now,

$\sf{tan \: 50 ^{ \circ} = \frac{hf}{30} } \\ \\ \sf{1.19 = \frac{hf}{30} } \\ \\ \sf{1.19 \times 30 = hf} \\ \\ \boxed{ \purple{ \sf{hf = 35.7 \: m}}}$

____________________________

(3).

Height of tower is GD.

So,

GD = 35.7 + 1.6 + 9.2

GD = 46.5 m

$\Large{\boxed{\orange{\sf{Height \: of \: tower \: = \: 46.5 \: m}}}}$