A man flies a kite with a 100 foot string. the angle of a string is 52 degrees. how length off the ground is the kite?
We want to view this as a triangle:
......x <--- lets say this is the kite
angle to kite = 52 degrees
............. ground
So you know the hypotenuse of this triangle is 100 ft. We want to find out the height. I don't know if you've been taught these acronyms: SOH CAH TOA. Most people have I'll refer to this. Out of these the only one you can use is SOH because opposite the hypotenuse is the height which is what you want to find. So fill in the values:
Sin52 = opposite/100
0.78 (about) = opposite/100
0.78*100 = opposite
78 feet = opposite
So the kite is about 78 feet above the ground. If you multiply the actual sin value (with all the decimals) with 100 you're get a more accurate result. I just don't have a calculator handy.
To find the height of the kite, we can use trigonometry. Given that the length of the string is 100 feet and the angle of the string with the ground is 52 degrees, we need to find the height of the kite.
Let's label the height of the kite as "h". In a right-angled triangle, the height can be found using the formula:
h = length of string * sin(angle)
Using this formula, we can calculate the height of the kite as follows:
h = 100 feet * sin(52 degrees)
To find the value of sin(52 degrees), we can use a scientific calculator or an online calculator. The sin(52 degrees) is approximately 0.7880.
Therefore, the height of the kite is:
h = 100 feet * 0.7880
h ≈ 78.80 feet
So, the kite is approximately 78.80 feet off the ground.
To determine the length of the string off the ground, we need to use trigonometry. In this case, we can use the sine function. The sine function relates the ratios of the opposite side to the hypotenuse in a right triangle.
Here's how we can calculate it:
Step 1: Draw a diagram of the situation. Label the angles and sides of the triangle. Let's say the height of the kite from the ground is represented by "h," and the length of the string is 100 feet.
^
|\
h | \ 52°
| \
|___\
100 ft
Step 2: Identify the relevant sides of the triangle. The angle of 52 degrees is opposite the height of the kite (h), and the hypotenuse is the length of the string (100 ft).
Step 3: Use the sine function to find the length of the side opposite the given angle:
sin(52°) = h / 100
Step 4: Rearrange the formula to solve for "h," which represents the height off the ground:
h = 100 * sin(52°)
Step 5: Calculate the value:
h = 100 * 0.788 (rounded to 3 decimal places)
h ≈ 78.8 feet
Therefore, the kite is approximately 78.8 feet off the ground.