Question

1. in δdef, fe = 13 and m∠f = 34. find df to the nearest tenth.

15.7
10.8
16.2
11.1

Explanation:

Step1: Identify the trigonometric ratio

In right triangle \( \triangle DEF \), \( \angle E = 90^\circ \), \( FE = 13 \) (adjacent side to \( \angle F \)), and we need to find \( DF \) (hypotenuse). The cosine of \( \angle F \) is defined as \( \cos(\angle F)=\frac{\text{adjacent}}{\text{hypotenuse}} \). So, \( \cos(34^\circ)=\frac{FE}{DF} \).

Step2: Solve for \( DF \)

We know \( FE = 13 \) and \( \angle F = 34^\circ \). From the cosine formula, we can rearrange to get \( DF=\frac{FE}{\cos(34^\circ)} \).
Using a calculator, \( \cos(34^\circ)\approx0.8290 \). Then \( DF = \frac{13}{0.8290}\approx15.7 \).

Answer:

15.7