In a right triangle DEF where the angle at E is 90°, we are given that DF = 31 m and the angle at F is 31°.
Since the angle at E is 90°, we have a right triangle and can use trigonometric ratios to find the length of side DE.
Using the sine ratio:
\(\sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}}\)
Given the angle at F is 31° and the opposite side is DE, we have:
\(\sin(31°) = \frac{DE}{DF}\)
Solving for DE:
\(DE = DF \cdot \sin(31°)\)
Substituting the values:
\(DE = 31 \cdot \sin(31°)\)
Using a calculator, you can find the value of \(\sin(31°)\) (approximately 0.5150):
\(DE = 31 \cdot 0.5150 \approx 15.965\)
So, the length of side DE is approximately 15.965 meters.