What is the value of cosC AB=8 BC=15 CA=17

The value of cos C = 15/17

Step-by-step 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