A boy lets out 150 feet of kite string. the string makes an angle of 64 degrees with the ground. his hands hold the reel 3 feet above the ground. assuming the string is straight, how high above the ground is the kite? round to the nearest tenth of a foot
well, you can see that
(h-3)/150 = sin64°
To find the height of the kite above the ground, we can use trigonometry. Let's denote the height of the kite as "h".
In this scenario, we have a right triangle formed by the kite string, the height of the reel, and the height of the kite above the ground.
Using trigonometric functions, we know that the tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the tangent of the angle of 64 degrees is equal to the height of the kite (opposite side) divided by the distance between the boy and the kite (adjacent side).
So, we can write the equation as follows:
tan(64 degrees) = h / (150 feet + 3 feet)
Now, we can solve for "h". First, let's calculate the total length of the kite string:
150 feet + 3 feet = 153 feet
Now, rearrange the equation and solve for "h":
h = tan(64 degrees) * 153 feet
Using a calculator, we can find:
h ≈ 165.11 feet
Therefore, the kite is approximately 165.1 feet above the ground, rounded to the nearest tenth of a foot.