Question

Enter the number that belongs in the green box.

Answer 1

? ≈ 9.40

Explanation:

using the sine rule in the triangle

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

where a is the side opposite ∠ A and b the side opposite ∠ B

we require the third angle in the triangle

third angle = 180° - (34 + 118)° = 180° - 152° = 28° , then

a = 5 , ∠ A = 28° , b = ? , ∠ B = 118°

`(5)/(sin28)` =
`(?)/(sin118)` ( cross- multiply )

? × sin28° = 5 × sin118° ( divide both sides by sin28° )

? =
`(5sin118)/(sin28)` ≈ 9.40 ( to the nearest hundredth )