find m∠f.\nwrite your answer as an integer or as a decimal rounded to the nearest tenth.\nm∠f = □°

Explanation:

Step1: Identify the cosine - ratio

In right - triangle $DEF$ with right - angle at $D$, $\cos(F)=\frac{DF}{EF}$. Here, $DF = 6$ and $EF=7$.

Step2: Calculate the cosine of angle $F$

$\cos(F)=\frac{6}{7}\approx0.857$.

Step3: Find the measure of angle $F$

$F=\cos^{- 1}(\frac{6}{7})$. Using a calculator, $F=\cos^{-1}(0.857)\approx31.0^{\circ}$.

Answer:

$31.0$