Question

If the sides of an acute angle triangle ABC are 7cm, 8cm and 9cm, find the value of sec C?
1. 3/2
2. 2/3
3. 1/3
4. 2

Answer 1

Correct Answer - Option 1 : 3/2

Given:

Side AB = 7 cm

BC = 8 cm

AC = 9 cm

Identity used:

If the sides of triangle ABC are

AB = c

BC = a

AC = b

Cosine rule;

Cos C = (a² + b² - c²)/2ab

Sec θ = 1/cos θ 

Calculation:

In triangle ABC;

Cos C = (82 + 92 - 72)/(2 × 8 × 9)

⇒ (64 + 81 - 49)/144

⇒  96/144 = 2/3

∴ The value of Sec C = 3/2