Question

If the shadowofa tower is√3 timew height, then find the
angleof the sun's altitude?​

Answer 1

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

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

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

$\green{\underline \bold{Given :}} \\ \tt: \implies Shadow \: of \: tower = \sqrt{3} \: times \: height \: of \: tower \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Angle \: of \: sun \: altitude= ?$

• According to given question :

$\tt \circ \: let \: height \: of \: tower \: be \: x \\ \\ \tt \circ \: length \: of \: shadow = \sqrt{3} x \\ \\ \tt \circ \: let \: \alpha \: be \: the \: angle \: of \:elevation \: of \: tower \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies tan \: \alpha = \frac{p}{b} \\ \\ \tt : \implies tan \: \alpha = \frac{height \: of \: tower}{length \: of \: shadow} \\ \\ \tt : \implies tan \: \alpha = \frac{ x }{ \sqrt{3}x } \\ \\ \tt : \implies tan \: \alpha = \frac{1}{ \sqrt{3} } \\ \\ \tt : \implies tan \: \alpha =tan \: 30 \degree \\ \\ \green{\tt : \implies \alpha =30 \degree} \\ \\ \green{\tt \therefore Angle \: of \: elevation \: of \: tower \: is \: 30 \degree}$

Answer 2

GIVEN :-

The shadow of a tower is √3 times the height of the tower.

TO FIND :-

The angle of Sun's altitude (the angle of elevation).

SOLUTION :-

Let the height of the tower be x.

Then the length of the shadow of the tower = √3x.

(AB represents the tower and BC represents its shadow)

We know,

tanθ = Perpendicular/Base

⇒tanθ = x/√3x

⇒tanθ = 1/√3

⇒tanθ = tan 30°

⇒θ = 30°

∴ Therefore, the angle of Sun's altitude is 30°.