Answer:
Step-by-step explanation:
height of the kite (82 feet), which is 86 feet. The length of the triangle's hypotenuse is the length of the string, which is 100 feet. Now, let's use the tangent function to find the angle of elevation (θ). Tangent is defined as the ratio of the opposite side (height) to the adjacent side (distance). So we have: tan(θ) = height / distance Substituting the values we know: tan(θ) = 86 / 100 Now, we can use the inverse tangent function (arctan) to find the angle: θ = arctan(86 / 100) Using a calculator, we find: θ ≈ 42.7 degrees Therefore, the angle of elevation from the man to the kite is approximately 42.7 degrees.
Work Shown
sin(angle) = opposite/hypotenuse
sin(Θ) = 82/100
sin(Θ) = 0.82
Θ = sin⁻¹(0.82)
Θ ≈ 55.08479375256
Θ ≈ 55.085
Round the approximate answer however needed.
Refer to the diagram below.
