The length of a string between a kite and a point on the roof of a building 10 m high is 180 m. If the string makes an angle A with the level ground such that tan A = $\frac{4}{3}$ . How high is the kite from the ground?

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Solution

We can take angle A with ground level, same as angle with building level (corresponding angles)

tan A = $\frac{B C}{A B}$ = $\frac{4}{3}$

If $A B = 3 x$ & $B C = 4 x$

Then $A C = 5 x$ (using pythagoras theorem)

It is given that $A C = 180 m$ (String length)

$5 x = 180$

$x = 36 m$

Hence $B C = 4 x = 144 m$

But the point B is on top of building of height 10m

Hence height of kite from ground is 10 + 144 = 154 m

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The length of a string between a kite and a point on the roof of a building 10 m high is 180 m. If the string makes an angle A with the level ground such that tan A =43. How high is the kite from the ground?

The length of a string between a kite and a point on the roof of a building 10 m high is 180 m. If the string makes an angle A with the level ground such that tan A = $\frac{4}{3}$ . How high is the kite from the ground?