a kite is at height of 30 feet when 65 feet of string is out. if the string is in a straight line, find the angle that it makes with the ground. Round to the nearest tenth of a degree.
To solve this problem, we can use trigonometry. Let's consider the right triangle formed by the height of the kite, the length of the string, and the ground.
First, we need to find the length of the other side of the triangle. We can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
Let's represent the length of the other side as x:
x^2 + 30^2 = 65^2
Simplifying the equation:
x^2 + 900 = 4225
x^2 = 4225 - 900
x^2 = 3325
Taking the square root of both sides:
x ≈ √3325
x ≈ 57.7 feet
Now that we have the lengths of the two sides of the triangle (30 and 57.7 feet), we can find the angle θ that the string makes with the ground using the trigonometric function tangent:
tan(θ) = opposite side / adjacent side
tan(θ) = 30 / 57.7
θ = tan^(-1)(30 / 57.7)
Using a scientific calculator or an online trigonometry tool, we can find the inverse tangent (tan^(-1)) of 30 / 57.7:
θ ≈ 26.4°
Therefore, the angle that the string makes with the ground is approximately 26.4 degrees, rounded to the nearest tenth of a degree.