Answer:
The value of cos C = 15/17
Explanation:
* Lets revise the cosine rule
- In Δ ABC
# AB opposite to angle C
# BC opposite to angle A
# AC opposite to angle B
# ∠A between AB and AC
# ∠B between BA and BC
# ∠C between CA and CB
- Cosine rule is:
# AB² = AC² + BC² - 2(AC)(BC) cos∠C
# BC² = AC² + AB² - 2(AC)(AB) cos∠A
# AC² = AB² + BC² - 2(AB)(BC) cos∠B
* Lets solve the problem
∵ AB = 8 units
∵ BC = 15 units
∵ CA = 17 units
∵ AB² = AC² + BC² - 2(AC)(BC) cos∠C
- Add 2(AC)(BC) cos∠C to both sides
∴ AB² + 2(AC)(BC) cos∠C = AC² + BC²
- Subtract AB² from both sides
∴ 2(AC)(BC) cos∠C = AC² + BC² - AB²
- Divide two sides by 2(AC)(BC)
∴ cos∠C = (AC² + BC² - AB²)/2(AC)(BC)
- Substitute the values of AB , BC , AC to find cos∠C
∴ cos∠C = (17)² + (15)² - (8)²/2(17)(15)
∴ cos∠C = (289 + 225 - 64)/510
∴ cos∠C = 450/510 = 15/17
* The value of cos C = 15/17