Question

Enter the number that belongs in the green box

Answer 1

? ≈ 29.45°

Explanation:

using the Sine rule in the triangle

`(a)/(sinA)` =
`(b)/(sinB)` =
`(c)/(sinC)`

where a is the side opposite ∠ A

b is the side opposite ∠ Band c is the side opposite ∠ C

using the first pair of ratios

with a = 6 , ∠ A = ? , b = 11.89 and ∠ B = 103° , then

`(6)/(sin?)` =
`(11.89)/(sin103)` ( cross- multiply )

11.89 × sin? = 6 × sin103° ( divide both sides by 11.89 )

sin? =
`(6sin103)/(11.89)` , then

? =
`sin^(-1)` (
`(6sin103)/(11.89)` ) ≈ 29.45° ( to the nearest hundredth )