Question

find fg.

right triangle fge with right angle at g, hypotenuse fe = 4, angle at f is 49 degrees.

write your answer as an integer or as a decimal rounded to the nearest tenth.
fg =
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Explanation:

Step1: Identify trigonometric ratio

In right triangle \( FGE \), \( \angle F = 49^\circ \), hypotenuse \( FE = 4 \), and \( FG \) is adjacent to \( \angle F \). Use cosine: \( \cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}} \).
\( \cos(49^\circ)=\frac{FG}{4} \)

Step2: Solve for \( FG \)

Multiply both sides by 4: \( FG = 4 \times \cos(49^\circ) \)
Calculate \( \cos(49^\circ)\approx0.6561 \), so \( FG\approx4\times0.6561 = 2.6244 \), round to nearest tenth: \( 2.6 \)

Answer:

\( 2.6 \)