Questions: Find the length DE.

Find the length DE.
Transcript text: Find the length $D E$.
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Solution

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Solution Steps

Step 1: Analyze the given information

We are given a right triangle $\triangle DEF$ with $\angle E = 90^\circ$. We are given $FE = 17$ m and $\angle D = 51^\circ$. We are asked to find the length of $DE$.

Step 2: Use trigonometric ratios

We can use the tangent function, which relates the opposite side and the adjacent side of a right triangle to the angle. In this case, we have $\tan(\angle D) = \frac{EF}{DE}$.

Step 3: Substitute the given values

Substituting the given values, we have $\tan(51^\circ) = \frac{17}{DE}$.

Step 4: Solve for DE

We can rearrange the equation to solve for $DE$: $DE = \frac{17}{\tan(51^\circ)}$.

Step 5: Calculate the value

Using a calculator, we find that $\tan(51^\circ) \approx 1.2349$. $DE = \frac{17}{1.2349} \approx 13.766 \approx 13.8$ m.

Final Answer

\\(\boxed{13.8 \text{ m}}\\)

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