A kite is flying 98 ft off the ground, and its string is pulled taut. The angle of elevation of the kite is 59°. Find the length of the string. Round your answer to the nearest tenth.
Question
A kite is flying 98 ft off the ground, and its string is pulled taut. The angle of elevation of the kite is 59°. Find the length of the string. Round your answer to the nearest tenth.
Solution
To solve this problem, we can use the trigonometric function of tangent. The tangent of an angle in a right triangle is defined as the ratio of the opposite side to the adjacent side. In this case, the opposite side is the height of the kite from the ground (98 ft) and the adjacent side is the length of the string we are trying to find.
The formula for tangent is:
tan(θ) = opposite / adjacent
We can rearrange this formula to solve for the adjacent side (the length of the string):
adjacent = opposite / tan(θ)
Substituting the given values:
adjacent = 98 ft / tan(59°)
Now, we just need to calculate the value. Remember to use the degree mode in your calculator when calculating the tangent of 59°.
adjacent ≈ 98 ft / 1.6643 ≈ 58.9 ft
So, the length of the string is approximately 58.9 ft.
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