A kite with a string 30 meters long makes an angle of elevation of 60° with the ground, assuming the string is straight, how high is the kite? Round your answer to the nearest tenth. Do not include units.
height/30 = sin60
height = 30sin60 = ....
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To find the height of the kite, we need to use some trigonometry.
First, let's label the triangle formed by the string and the height of the kite. The angle of elevation of 60° is opposite the height of the kite, which we'll call h. The length of the string is the hypotenuse of the triangle, which we'll call 30 meters.
We can use the sine function to solve for the height of the kite:
sin(60°) = opposite / hypotenuse
sin(60°) = h / 30
To solve for h, we can multiply both sides of the equation by 30:
30 * sin(60°) = h
To evaluate sin(60°), you can use a scientific calculator or look up the value in a trigonometric table. The sine of 60° is √3/2.
Substituting this value into the equation:
30 * (√3/2) = h
Simplifying:
15√3 = h
Therefore, the height of the kite is approximately 25.9808 meters when rounded to the nearest tenth.