Question

solve for x. round to the nearest tenth of a degree, if necessary.
triangle def with right angle at e, de = 6, ef = 6.8, angle at f is x degrees
answer attempt 1 out of 2
x = blank ° submit answer

Explanation:

Step1: Identify trigonometric ratio

In right triangle \( DEF \), \( \angle E = 90^\circ \), opposite side to \( \angle F \) (which is \( x^\circ \)) is \( DE = 6 \), adjacent side is \( EF = 6.8 \). So we use tangent: \( \tan(x) = \frac{\text{opposite}}{\text{adjacent}} = \frac{6}{6.8} \).

Step2: Calculate \( x \)

First, compute \( \frac{6}{6.8} \approx 0.8824 \). Then, take the arctangent: \( x = \arctan(0.8824) \). Using a calculator, \( x \approx 41.4^\circ \) (rounded to nearest tenth).

Answer:

\( 41.4 \)