Solving Word Problems with Trigonometry - Trigonometry - Free Printable

Explanation:
We are given a right triangle where:

- The hypotenuse (the slanted side) is 4000 meters.
- One of the acute angles is 22°.
- The side labeled x is opposite that 22° angle — it’s the vertical height.

In a right triangle, the sine of an angle equals:

\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}
\]

Here,
\(\theta = 22^\circ\),
opposite = \(x\),
hypotenuse = 4000 m.

So:

\[
\sin(22^\circ) = \frac{x}{4000}
\]

Now solve for \(x\):

\[
x = 4000 \times \sin(22^\circ)
\]

Let’s calculate \(\sin(22^\circ)\). Using a calculator (make sure it's in degree mode):

\[
\sin(22^\circ) \approx 0.3746
\]

Then:

\[
x = 4000 \times 0.3746 = 1498.4
\]

Rounded to the nearest meter (since the input was whole meters),
\(x \approx 1498\) meters.

Let me double-check:
- Is x opposite the 22° angle? Yes — the right angle is at the bottom right, so the vertical side is opposite the 22° angle at the bottom left.
- Did we use sine correctly? Yes — sine = opposite/hypotenuse.
- Calculator value: sin(22°) ≈ 0.3746065934 → ×4000 = 1498.426… → 1498 m (or possibly 1498.4 if decimals allowed).

Since no rounding instruction is given, and the problem uses whole numbers (4000 m, 22°), it’s reasonable to give the answer to the nearest meter.

Final Answer:
1498