The length of a string between a kite and a point on the ground is 90 metres If - Maths -

Question

The length of a string between a kite and a point on the ground
is 90 metres If the string makes an angle theeta with the ground
level such that tan theeta = 15/8, how high is the kite Assume that
there is no slack in the string

Priyanka Kedia · Accepted Answer

Let the height of the kite AB = h m Given, string makes an angle theta with the ground level such that $\tan θ = 15 / 8$ So, $\tan θ = \frac{15}{8} \Rightarrow \frac{A B}{B C} = \frac{15}{8} \Rightarrow A B = 15 k (1) a n d B C = 8 k$ Now, $I n r i g h t Δ A B C, {A C}^{2} = {A B}^{2} + {B C}^{2} \Rightarrow {(90)}^{2} = {(15 k)}^{2} + {(8 k)}^{2} \Rightarrow 8100 = 225 k^{2} + 64 k^{2} \Rightarrow 8100 = 289 k^{2} \Rightarrow k^{2} = \frac{8100}{289} \Rightarrow k = \frac{90}{17}$ Substitute value of k in equation (1), we get, $H e i g h t o f t h e k i t e A B = 15 k = 15 \times \frac{90}{17} = 79 41 m$ Hence, height of the kite is 79 41 m

The length of a string between a kite and a point on the ground is 90 metres . If the string makes an angle theeta with the ground level such that tan theeta = 15/8, how high is the kite. Assume that there is no slack in the string.