Question

determine the length of side d to the nearest tenth of a centimeter. select one: a. 10.7 cm b. 29.5 cm c. 27.7 cm d. 3.7 cm

Explanation:

Step1: Identify trigonometric relation

In right - triangle $\triangle FED$, $\sin F=\frac{DE}{DF}$. Given $\angle F = 20^{\circ}$ and $DE = 10.1$ cm, and we want to find $DF=d$.

Step2: Rearrange the formula

We can rewrite the formula as $d=\frac{DE}{\sin F}$.

Step3: Substitute values

Substitute $DE = 10.1$ cm and $\sin F=\sin20^{\circ}\approx0.342$ into the formula: $d=\frac{10.1}{0.342}\approx29.5$ cm.

Answer:

b. 29.5 cm