A kite is flying at an angle of elevation of about 40 degrees. All 80 meters of string have been let out. Ignoring the sag in the string, find the height of the kite nearest ten meters.
h/80 = sin40
To find the height of the kite, we can use trigonometry. Let's define the angle of elevation as θ and the height of the kite as h.
First, draw a right-angled triangle, representing the situation. The string of the kite is the hypotenuse of the triangle, and the height is the side opposite the angle of elevation.
Let's label the sides of the triangle:
- The hypotenuse (the string) = 80 meters
- The opposite side (the height) = h
- The adjacent side (the distance on the ground) = x (unknown)
Now, using the trigonometric ratio for the sine of an angle:
sin(θ) = opposite/hypotenuse
Plug in the values we know:
sin(40°) = h/80
To solve for h, we can rearrange the equation:
h = 80 * sin(40°)
Using a calculator, we can find sin(40°) ≈ 0.6428:
h ≈ 80 * 0.6428
h ≈ 51.424 meters
Therefore, the height of the kite is approximately 51.424 meters.