Question

triangle def contains right - angle e. if angle d measures 50° and its opposite side measures 7.6 units, what is the measure of side de? round your answer to the nearest hundredth.

Explanation:

Step1: Identify the trigonometric relation

In right - triangle DEF with right - angle at E, $\tan D=\frac{EF}{DE}$. We know $\angle D = 50^{\circ}$ and $EF = 7.6$ units.

Step2: Rearrange the formula to solve for DE

We can rewrite the formula as $DE=\frac{EF}{\tan D}$.

Step3: Substitute the values

Substitute $EF = 7.6$ and $\angle D=50^{\circ}$ into the formula. Since $\tan50^{\circ}\approx1.1918$, then $DE=\frac{7.6}{1.1918}$.

Step4: Calculate the value of DE

$DE=\frac{7.6}{1.1918}\approx6.38$ units.

Answer:

6.38 units