Q. 8

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

Answer :

Let AB be the height of kite.

**Given:**

**To find:** The length of AB.

**Formula Used:**

**Explanation:**

Let the height of string = “h” m

As we know,

In ΔPQR,

Perpendicular = PQ = 15

Base =QR = 8

According to Pythagoras theorem,

PR^{2} = PQ^{2} + QR^{2}

⇒ PR^{2} = 15^{2} + 8^{2}

⇒ PR^{2} = 225 + 64

⇒ PR^{2} = 289

⇒ PR = √289

⇒ PR = 17

As,

sin θ =

In ∆ABC,

17h = 90×15

⇒ 79.41 m

**Therefore, length of string = 79.41 m.**

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