Question

Length of the tight thread of a kite from a point on the ground is $85$ m. If thread subtends an angle $\theta$ with the ground such that $tan\theta =8/15$, then find the height at which kite is flying.

• A. $40m$
• B. $44m$
• C. $50m$
• D. $55m$

Answer 1

The correct option is A $40m$

Let the height at which the kite flies is AB = P m
Now $tan\theta =\frac{8}{15}=\frac{P}{B}$
Let P = $8xm,B=15xm$
$(85{)}^2=(8x{)}^2+(15x{)}^2$
$7225=64x^2+225x^2$
$7225=289x^2$
$17x=85\Rightarrow x=5$
Hence, $P=8x$ = $8\times 5=40$