Question

Brains kite is flying above a field at the end of 65 m of string. If the angle elevation to the kite measures 70 degrees and Brian is holding the kite 1.2 m off the ground. How high above the ground is the kite flying?

Answer 1

The height above the ground the kite is flying is 62.28 meters

Solution:

Given that Brains kite is flying above a field at the end of 65 m of string

The figure is attached below

ABC is a right angled triangle

Let AB be the height at which the kite is flying above the ground

AB = h = ?

Given that angle elevation to the kite measures 70 degrees

Thus angle C = 70 degrees

Brains kite is flying above a field at the end of 65 m of string

Therefore, AB = 65 meters

We know that,

$sin \theta = \frac{opposite}{hypotenuse}$

Here,

$\theta = 70^{\circ}$

Opposite = AB = h

Hypotenuse = AC = 65 meters

Therefore,

$sin 70 = \frac{h}{65}\\\\0.9397 = \frac{h}{65}\\\\h = 0.9397 \times 65\\\\h = 61.08$

To find the height above the ground we have to add 1.2 m to 61.08

height above the ground = 61.08 + 1.2 = 62.28 meters

Thus the height above the ground the kite is flying is 62.28 meters