Question

Enter the number that belongs in the green box

Answer 1

? ≈ 9.09

Explanation:

using the Sine rule in the triangle

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

where a, b , c are the sides opposite angles A , B , C

we require the third angle in the triangle

third angle = 180° - (51 + 109)° = 180° - 160° = 20°

then with

a = 4 , ∠ A = 20°

b = ? , ∠ B = 51°

`(4)/(sin20)` =
`(?)/(sin51)` ( cross- multiply )

? × sin20° = 4 × sin51° ( divide both sides by sin20° )

? =
`(4sin51)/(sin20)` ≈ 9.09 ( to the nearest hundredth )