A kite string is 65 metres long and makes an angle of 32 degrees with the ground. Calculate the height of the kite above the ground to the nearest metre.
h/65 = sin 32
To find the height of the kite above the ground, we can use trigonometry. In this case, we have a right triangle formed by the kite string, the height of the kite, and the distance from the kite to the ground.
Let's break down the given information:
- The kite string is 65 meters long.
- The angle between the kite string and the ground is 32 degrees.
We want to find the height of the kite above the ground. Let's call this height "h."
Now, we can use the trigonometric function tangent (tan) to calculate the height of the kite:
tan(angle) = opposite / adjacent,
where "opposite" represents the height of the kite, and "adjacent" represents the distance from the kite to the ground, which is 65 meters.
tan(32 degrees) = h / 65.
To isolate "h," we can rearrange the equation:
h = tan(32 degrees) * 65.
Now, let's calculate the height using this formula:
h ≈ tan(32) * 65.
Using a calculator, we find that tan(32 degrees) ≈ 0.6249.
Substituting this value into the equation:
h ≈ 0.6249 * 65 ≈ 40.56.
The height of the kite above the ground is approximately 40.56 meters, rounded to the nearest whole number, which is 41 meters.