Final answer:
To find the length of side e in triangle DEF, we calculated the remaining angle using the fact that the sum of angles in a triangle is 180° and applied the Law of Sines to set up a ratio involving the given information. After solving, we provide the length of e rounded to the nearest tenth.
Step-by-step explanation:
To find the length of e in triangle DEF, we can use the Law of Sines which relates the lengths of sides of a triangle to the sines of its opposite angles. The Law of Sines states that the ratio of the length of a side to the sine of its opposite angle is the same for all three sides of the triangle. In triangle DEF, we are given f = 33 inches, m∠ F = 140°, and m∠ D = 5°. The remaining angle, m∠ E, can be found since the sum of angles in any triangle is 180°. Therefore, m∠ E = 180° - 140° - 5° = 35°. Now we can set up the ratio as follows:
-
- sin F / f = sin E / e
-
- sin(140°) / 33 = sin(35°) / e
-
- e = 33 * sin(35°) / sin(140°)
After calculating the right side of the equation, we find the length of e, rounded to the nearest tenth of an inch.