Question

sam is flying a kite. the length of the kite string is 80 meters, and it makes an angle of 75° with the ground. the height of the kite from the ground is [ ]meters?

Answer 1

77.27 meters.

Explanation:

Please find the attachment.

Let h be the the height of the kite from the ground.

We have been given that the length of the kite string is 80 meters, and it makes an angle of 75° with the ground.

We can see from our attachment that the string of kite, angle of elevation form a right angle with respect to ground.

Since we know that sine relates the opposite side and hypotenuse of a right triangle, so we can find 'h' as shown below:

`\text{sin}(75^(\circ))=(h)/(80)`

`0.965925826289=(h)/(80)`

`0.965925826289* 80=(h)/(80)* 80`

`77.27406610312=h`

`h\approx 77.27`

Therefore, the height of the kite from the ground is 77.27 meters.

Answer 2

The height of the kite from the ground can be obtained using trigonometry. As the string is 80 meters long, this is treated as the hypotenuse. Taking the sine of the angle would yield us the height of the kite from the ground. This is shown below:

Let: h = height of the kite from the ground

sin 75 = h / 80
h = 80 sin 75
h = 77.27 meters

Therefore, the kite is 77.27 meters from the ground.