Final answer:
To find the length of BC in triangle ABC with angle A at 45 degrees, side AB at 20, and side AC at 15, we use the law of cosines and round the result to the nearest tenth.
Step-by-step explanation:
To find the length of BC in triangle ABC where angle A is 45 degrees, AB is 20, and AC is 15, we can use the law of cosines. Since triangle ABC is not a right triangle we cannot directly apply the Pythagorean theorem, but instead, we must apply the law of cosines:
BC² = AB² + AC² - 2(AB)(AC)cos(A)
Plugging in the values:
BC² = 20² + 15² - 2(20)(15)cos(45°)
BC² = 400 + 225 - 600(cos(45°))
Since cos(45°) = √2/2,
BC² = 625 - 600(√2/2)
BC² = 625 - 300√2
BC = √(625 - 300√2)
Calculating the radical expression gives us the length of BC. After performing this calculation, we round the result to the nearest tenth to obtain the final answer.