Applied Trigonometry Problems Worksheet for 9th - 12th Grade ... - Free Printable

Let’s solve Example #1 step by step.

We are told:
- The airplane takes off at an angle of 7° from the ground.
- It has traveled 500 feet along its flight path (this is the hypotenuse of a right triangle).
- We need to find how high it is above the ground — that’s the side opposite the 7° angle.

This is a trigonometry problem using sine, because:

> sin(θ) = opposite / hypotenuse

Here:
- θ = 7°
- hypotenuse = 500 ft
- opposite = height we want to find → let’s call it “h”

So:

sin(7°) = h / 500

Now solve for h:

h = 500 × sin(7°)

Use a calculator to find sin(7°). Make sure your calculator is in degree mode.

sin(7°) ≈ 0.121869

Then:

h ≈ 500 × 0.121869 ≈ 60.9345

Round to the nearest foot → 61 feet

✔ Double-check:
Is this reasonable? A 7° angle is shallow, so after 500 feet forward/up, being about 61 feet up makes sense. If it were 30°, it would be 250 feet up — so 7° should be much less. Yes, 61 is reasonable.

Final Answer:
61