Question

use the table to approximate ( mangle d ) in the triangle below.
triangle efd with right angle at f, ef = 6.1, ed = 6.7 (or relevant side labels)
choose 1 answer:
a ( 55^circ )
b ( 65^circ )
c ( 75^circ )

Explanation:

Step1: Identify triangle type and trigonometric ratio

Triangle \( DEF \) is a right triangle with \( \angle F = 90^\circ \). We know the lengths of the opposite side (\( EF = 6.1 \)) and the hypotenuse (\( ED = 6.7 \)) relative to \( \angle D \). The sine ratio is \( \sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}} \), so \( \sin(\angle D)=\frac{EF}{ED}=\frac{6.1}{6.7} \).

Step2: Calculate the sine value

\( \frac{6.1}{6.7}\approx0.9104 \).

Step3: Find the angle with this sine value

We know that \( \sin(65^\circ)\approx0.9063 \), \( \sin(75^\circ)\approx0.9659 \), and \( \sin(55^\circ)\approx0.8192 \). The value \( 0.9104 \) is closest to \( \sin(65^\circ) \).

Answer:

B. \( 65^\circ \)