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...
A.20.27
B.61
C.77.27
C. 77.27METERS
77.27
You will have a right triangle with the 80 meters on the hypotenuse and the x on the side opposite the 75 degree angle.
Using Trig:
x/80 which is opposite over hypotenuse
equal to sin of 75 degrees.
Find the sin of 75 and multiply it by 80 to find x.
To find the height of the kite from the ground, we can use trigonometry.
In this scenario, the length of the kite string represents the hypotenuse of a right-angled triangle, and the height of the kite from the ground represents the opposite side of the triangle.
First, let's identify the relevant sides of the triangle:
- The length of the kite string, which is the hypotenuse, is 80 meters.
- The angle the kite string makes with the ground is 75°.
Now, we can use the trigonometric function "sine" to find the height of the kite.
The sine function relates the angle of a right-angled triangle to the lengths of its sides. In this case, we want to find the length of the opposite side (height) of the triangle.
The sine function is defined as:
sin(angle) = opposite/hypotenuse
To find the height (opposite side), we rearrange the formula:
opposite = sin(angle) * hypotenuse
Substituting in the values we have:
opposite = sin(75°) * 80
You can calculate sin(75°) using a calculator or trigonometric tables.
Using a calculator, sin(75°) is approximately 0.9659.
Calculating the height:
opposite = 0.9659 * 80
= 77.272
Therefore, the height of the kite from the ground is approximately 77.272 meters.
The correct answer is C. 77.27.