Question

Enter the number that belongs in the green box

Answer 1

Answer: 12.34

Explanation:

This is not a right triangle so you need to use Law of Cos:

c² = a² + b² - 2ab(cos C)

>Where capital C is the angle across from side lowercase c. a and b are sides

a=7

b=12

C=12

c=?

c² = 7² + 12² - 2(7)(12) cos 76

c² = 49 + 144 - 168cos 76

c² = 193 - 168cos 76

c² = 152.357

c = 12.34

Answer 2

? ≈ 12.34

Explanation:

using the Cosine rule in the triangle

a² = b² + c² - 2bc cosA

where b and c are known and A is the angle between them

here b = 12 , c = 7 , ∠ A = 76° , then

?² = 12² + 7² - ( 2 × 12 × 7 × cos76° )

= 144 + 49 - ( 168 × cos76°)

= 193 - 40.643

= 152.357 ( take square root of both sides )

? =
`√(152.357)` ≈ 12.34 ( to the nearest hundredth )