Question

I have two Law Of Sines Problems that I need to Help Solved! Please!!

give me a minute to upload the pictures


20 points if answer correct

Answer 1

From figure A

The value of ∠ B = 75.74° , ∠ C = 70.26° and AB = 27.37

From figure B

The value of ∠ A = 42.8° , ∠ B = 106.2° and AC = 30.04

Explanation:

Given first figure as :

AC = 28.2

BC = 16.5

∠ A = 34°

Let AB = c

From law of sines

`(a)/(Sin A)` =
`(b)/(Sin B)` =
`(c)/(Sin C)`

Or,
`(a)/(Sin A)` =
`(b)/(Sin B)`

or,
`(16.5)/(Sin 34)` =
`(28.2)/(Sin B)`

Or, 29.506 =
`(28.2)/(Sin B)`

Or, Sin B =
`(28.2)/(29.5)`

Or, Sin B = 0.955

∴ ∠B =
`Sin^(-1)` 0.955

I.e∠ B = 75.74

Now, ∠ C = 180° - ( ∠A + ∠B )

Or, ∠ C = 180° - ( 34° + 75.74° )

Or, ∠ C = 70.26°

Now, Again

`(b)/(Sin B)` =
`(c)/(Sin C)`

so,
`(28.2)/(Sin 75.74)` =
`(c)/(Sin 70.26)`

Or,
`(28.2)/(0.9691)` =
`(c)/(0.9412)`

Or, c = 29.09 × 0.9412

∴ c = 27.37

I.e AB = 27.37

Hence, The value of ∠ B = 75.74° , ∠ C = 70.26° and AB = 27.37

From figure second

Given as :

AB = c= 12

BC = a = 16

∠ C = 31°

let AC = b

From law of sines

`(a)/(Sin A)` =
`(b)/(Sin B)` =
`(c)/(Sin C)`

Or,
`(a)/(SinA )` =
`(c)/(Sin C)`

or,
`(16)/(Sin A)` =
`(12)/(Sin 31)`

or,
`(16)/(Sin A)` =
`(12)/(0.51)`

Or,
`(16)/(Sin A)` = 23.52

∴ Sin A =
`(16)/(23.52)`

I.e Sin A = 0.68

Or, ∠ A =
`Sin^(-1)` 0.68

or, ∠ A = 42.8°

Now, ∠ B = 180° - ( 31° + 42.8° )

Or, ∠ B = 106.2°

Now,
`(b)/(Sin B)` =
`(c)/(Sin C)`

or,
`(b)/(Sin 106.2)` =
`(16)/(Sin 31)`

Or,
`(b)/(0.96)` =
`(16)/(0.51)`

or, b = 31.3×0.96

∴ b = 30.04

Hence The value of ∠ A = 42.8° , ∠ B = 106.2° and AC = 30.04

Answer