Final answer:
To find the length of side e in triangle DEF with given sides and angle, the Law of Cosines is applied, yielding e approximately equal to 105 cm after calculation.
Step-by-step explanation:
To find the length of side e in triangle DEF, where f = 65 cm, d = 88 cm, and ∠e=85°, we can use the Law of Cosines. The Law of Cosines states that c² = a² + b² - 2abcos(γ), where c is the side opposite γ and a and b are the other two sides of the triangle. In this case, we want to find e, so we rearrange the formula to solve for e² = f² + d² - 2fd*cos(85°).
After calculating: e² = 65² + 88² - 2*65*88*cos(85°), we take the square root to get the length of e, rounding to the nearest centimeter. Let's complete the calculation:
- e² = 4225 + 7744 - 2*65*88*0.0872,
- e² ≈ 11969 - 994,
- e = √(10975) ≈ 104.76 cm,
- So, e ≈ 105 cm to the nearest centimeter.