Ruth is flying a kite. Her hand is 3 feet above ground level and is holding the end of a 375 foot long kite string, which makes an angle of 64° with the horizontal. How high is the kite above the ground? (Round your answer to one decimal place.)
height/375 = sin 64°
height = 375 sin 64°
= ...
find the above, then add 3 feet for the "above ground".
To find the height of the kite above the ground, we can use trigonometry. Specifically, we will use the sine function.
The sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse.
In this case, the height of the kite is the side opposite the angle of 64°, and the length of the kite string (375 feet) is the hypotenuse.
Let's calculate the height of the kite using the sine function:
sin(64°) = height of kite / length of kite string
Rearranging the equation, we get:
height of kite = sin(64°) * length of kite string
Now, let's plug in the values:
height of kite ≈ sin(64°) * 375
Using a scientific calculator, we find:
height of kite ≈ 0.8988 * 375
height of kite ≈ 337.65
Therefore, the height of the kite above the ground is approximately 337.6 feet.