A man standing on the deck of a ship is flying a kite. The ship deck is 30 feet above the water. The kite string is 75 feet long, and the kite flying at an angle of elevation of 60 degrees. How high above the water is the kite?
sintheta = opposite side / hypotenuse
sin(60)= (height the kite is above the boat)/ 75
75xsin60 = height of kite above boat
64.95 feet = height of kite above boat
Now you need to add the height of the boat deck from the water to your 64.95 to get the height of the kite above the water : )
h = 30 + 75*sin60 = 94.95 Ft. above water.
To find the height of the kite above the water, we need to use trigonometry.
First, we can define the given information:
- The height of the ship deck is 30 feet.
- The length of the kite string is 75 feet.
- The angle of elevation of the kite is 60 degrees.
To solve the problem, we can use the sine function, which relates the lengths of the sides of a right triangle. In this case, the sine function can be used to find the opposite side (the height of the kite) in relation to the given angle and the hypotenuse (the length of the kite string).
The formula for the sine function is:
sin(angle) = opposite / hypotenuse
Let's plug in the given values into the equation:
sin(60 degrees) = height / 75 feet
Now, we can solve for the height of the kite:
height = sin(60 degrees) * 75 feet
To calculate this, we can use a calculator or a table of trigonometric values. The sine of 60 degrees is √3 / 2, which is approximately 0.866.
height = 0.866 * 75 feet
height ≈ 64.95 feet
Therefore, the kite is approximately 64.95 feet above the water.