Trigonometry! #115

Geometry Level 1

The length of a string between a kite and a point on the ground is 85 m 85m . If the string makes an angle θ \theta with the level ground such that tan ⁡ θ = 15 8 \tan\theta=\frac{15}{8} , how high is the kite?

Enter your answer in m m , the number only.

This problem is part of the set Trigonometry .


The answer is 75.

Omkar Kulkarni by Omkar Kulkarni , 22, India

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1 solution

Nishant Kumar
Feb 15, 2015

Now tan θ=AC/CB=b/a, ,as tan θ =15/8, ,therefore b/a=15/8 ,Now it is sure that b and a are not equal to 15 and 8 because they are not Pythagoras triplet but they must be equal to their multiple. So let the numbers be 15x and 8x

So (15x)^2+(8x)^2=85^2 , 225x^2+64x^2=7225 289x^2=7225

now x^2=7225/289 ,,, x^2=25 , and x=5 Therefore the height of the kite is AC=b=15x=15*5=75m

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