Question

Calculate the side lengths a and b to two decimal places

Answer 1

E

Explanation:

using the Sine rule in Δ ABC

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

where a is the side opposite ∠ A , b opposite ∠ B , c opposite ∠ C

we require to calculate ∠ C

∠ C = 180° - (64 + 85)° = 180° - 149° = 31°

then to find a , using

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

`(a)/(sin64)` =
`(9.3)/(sin31)` ( cross- multiply )

a × sin31° = 9.3 × sin64° ( divide both sides by sin31° )

a =
`(9.3sin64)/(sin31)` ≈ 16.23 ( to 2 decimal places )

then to find b , using

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

`(b)/(sin85)` =
`(9.3)/(sin31)` ( cross- multiply )

b × sin31° = 9.3 × sin85° ( divide both sides by sin31° )

b =
`(9.3sin85)/(sin31)` ≈ 17.99 ( to 2 decimal places )