Question

Find the angle of elevation of the top of a tower from a point on the ground, which is 30 m

away from the foot of a tower of height 10
$\sqrt{3}$
m.​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Angle\:of\:elevation=30\degree}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given:}} \\ \tt: \implies Height \: of \: tower = 10 \sqrt{3} \: m \\ \\ \tt: \implies Distance \: between \: foot \: of \: the \: tower = 30 \: m \\ \\ \red{\underline \bold{To \: Find:}}\\ \tt: \implies Angle \: of \: elevation = ?$

• According to given question :

$\tt \circ \: Let \: angle \: of \: elevation \: be \: \theta \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies tan \: \theta = \frac{perpendicular}{base} \\ \\ \tt: \implies tan \: \theta = \frac{10 \sqrt{3} }{30} \\ \\ \tt: \implies tan \: \theta = \frac{ \sqrt{3} }{3} \\ \\ \tt: \implies tan \: \theta = \frac{1}{ \sqrt{3} } \\ \\ \tt: \implies tan \: \theta = tan \: 30 \degree \\ \\ \green{\tt: \implies \theta = 30 \degree}\\\\ \green{\tt\therefore Angle\:of\:elevation\:from\:top\:of\:tower\:to\:ground\:is\:30\degree}$

Answer 2

$\tt{\huge{\orange { Hello!!! }}} B.Q$

QUESTION :

Find the angle of elevation of the top of a tower from a point on the ground, which is 30 m

Find the angle of elevation of the top of a tower from a point on the ground, which is 30 maway from the foot of a tower of height 10

Find the angle of elevation of the top of a tower from a point on the ground, which is 30 maway from the foot of a tower of height 10 $\sqrt{3}$

Find the angle of elevation of the top of a tower from a point on the ground, which is 30 maway from the foot of a tower of height 10 $\sqrt{3}$m.

SOLUTION :

This question can be easily solved by using Trigonometric Identities.

Here, the following information is given :

The height of the tower is 10√ 3m.

The base of the tower is 30 m.

Let the angle of elevation be X °

We know that :

Tan X = Perpendicular / Base

=> 10 √ 3 / 30

=> √ 3 / 3

=> √ 3 / 3 ÷ √ 3 / √ 3

=> 1 / √ 3

Tan X = 1 / √ 3

X = tan ^ -1 ( 1 / √ 3 )

=> X = 30 °

Hence the angle of elevation is 30°>>>>[ A ]

ADDITIONAL INFORMATION :

Sin => Perpendicular / Hypotenuse

Cos => Base / Hypotenuse

Cot => Base / Perpendicular

Cosec => Hypotenuse / Perpendicular

Sec => Hypotenuse / Base