Looking at Problem 4, I can see it involves a kite flying in the sky. The diagram shows a right triangle where the kite string is the hypotenuse, the height of the kite is the vertical side (opposite), and we need to find the angle of elevation from the person holding the string to the kite.
From the problem, I can determine that:
- The kite string (hypotenuse) = 100 feet
- The height of the kite (opposite side) = 50 feet
To find the angle of elevation θ, I can use the sine function:
sin(θ) = opposite/hypotenuse = 50/100 = 0.5
Therefore, θ = arcsin(0.5)
I know that arcsin(0.5) = 30 degrees (since sin(30°) = 0.5).
So the angle of elevation from the person holding the string to the kite is 30 degrees.
Let me summarize all the solutions:
Problem 1: A 12-foot ladder with its base 3 feet from the wall.
- We have adjacent = 3 feet, hypotenuse = 12 feet
- cos(θ) = 3/12 = 0.25
- θ = arccos(0.25) ≈ 75.5 degrees
Problem 2: A 30-foot flagpole casting a 40-foot shadow.
- We have opposite = 30 feet, adjacent = 40 feet
- tan(θ) = 30/40 = 0.75
- θ = arctan(0.75) ≈ 36.9 degrees
Problem 3: A 10-foot ramp rising 2 feet.
- We have opposite = 2 feet, hypotenuse = 10 feet
- sin(θ) = 2/10 = 0.2
- θ = arcsin(0.2) ≈ 11.5 degrees
Problem 4: A kite at 50 feet height with a 100-foot string.
- We have opposite = 50 feet, hypotenuse = 100 feet
- sin(θ) = 50/100 = 0.5
- θ = arcsin(0.5) = 30 degrees
These are the solutions to all four problems on the worksheet.
Parent Tip: Review the logic above to help your child master the concept of trig story problems worksheet.
