Question

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

Explanation:

Step1: Identify trigonometric ratio

In right - triangle $DEF$ with right - angle at $F$, we use the cosine ratio. $\cos D=\frac{DF}{DE}$. Here, $DF = 6.1$ and $DE=6.7$. So, $\cos D=\frac{6.1}{6.7}\approx0.9104$.

Step2: Use inverse cosine

We know that $D=\cos^{- 1}(0.9104)$. Using a calculator or a trigonometric table, we find the angle whose cosine is approximately $0.9104$.

Answer:

A. $24.4^{\circ}\approx25^{\circ}$ (closest to the options, actual value from $\cos^{-1}(0.9104)\approx24.4^{\circ}$, and among the given options, the closest is A considering approximation in the table - based context)