Question

use the table to approximate m∠d in the triangle below. choose 1 answer: a 55° b 65° c 75°

Explanation:

Step1: Recall sine - ratio formula

In right - triangle $\triangle DEF$ with $\angle F = 90^{\circ}$, $\sin D=\frac{EF}{DE}$.

Step2: Substitute side - lengths

Given $EF = 6.1$ and $DE=6.7$, then $\sin D=\frac{6.1}{6.7}\approx0.9104$.

Step3: Use inverse - sine function

$D=\sin^{- 1}(0.9104)$. Using a calculator or a trigonometric table, we find that $D\approx65^{\circ}$.

Answer:

B. $65^{\circ}$