Question

The angle of elevation of a kite is 60⁰ and the length of the string is 40√3 then find the height of the kite from the grounds ?​

Answer 1

        $\text{\huge \bf \underline{Answer:}}$

        $\text{In the attachment below:}$

        $\text{Angle of Elevation} = \angle{C} = 60^{\circ}$

        $\text{Length of string} = AC = 40\sqrt3 \: m$

        $\text{Height of the kite from the ground} = AB$

        $\text{We know that, }\text{Sin} = \dfrac{\text{Perpendicular}}{\text{Hypotenuse}}$

$\implies \: \text{Sin60} = \text{SinC}$

        $\text{We know that, }\text{Sin60} = \dfrac{\sqrt3}{2}$

$\implies \: \dfrac{\sqrt3}{2}= \dfrac{AB}{AC}$

$\implies \: \dfrac{\sqrt3}{2}= \dfrac{AB}{40\sqrt3}$

$\implies \: \sqrt3\times40\sqrt3 = AB\times2$

$\implies \: 120 = 2AB$

$\implies \: \dfrac{120}{2} = AB$

$\implies \: 60 \: m = AB$

$\implies \: \boxed{\boxed{\text{Height of the kite from the ground} = 60 \: m}}$