Question

DO NOT WRITE IN THIS AREA 19 Solve 1 1 4 Give your answer in the form a +b√√2 where a and bare fractions.​

Answer 1

sin ABC =
`(325)/(1070)`

Explanation:

using the Sine Rule in triangle ABC

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

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

From the triangle

a = 10.7 , b = 6.5 and ∠ A = 30°

∠ B = ∠ ABC has to be found

Note that sin30° = 0.5

substituting values into the first 2 ratios of the Sine Rule

`(10.7)/(sin30)` =
`(6.5)/(sinB)` ( cross- multiply )

10.7 × sin B = 6.5 × sin30° = 6.5 × 0.5 = 3.25 ( divide both sides by 10.7 )

sin B =
`(3.25)/(10.7)` ( multiply numerator and denominator by 100 )

sin B =
`(325)/(1070)`