Question

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

Answer 1

Answer:

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

Step-by-step explanation:

Given first figure as :

AC = 28.2

BC = 16.5

∠ A = 34°

Let AB = c

From law of sines

$\dfrac{a}{Sin A}$ = $\dfrac{b}{Sin B}$ = $\dfrac{c}{Sin C}$

Or, $\dfrac{a}{Sin A}$ = $\dfrac{b}{Sin B}$

or, $\dfrac{16.5}{Sin 34}$ = $\dfrac{28.2}{Sin B}$

Or,  29.506 =  $\dfrac{28.2}{Sin B}$

Or, Sin B =  $\dfrac{28.2}{29.5}$  

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

$\dfrac{b}{Sin B}$ = $\dfrac{c}{Sin C}$

so,  $\dfrac{28.2}{Sin 75.74}$ = $\dfrac{c}{Sin 70.26}$

Or,   $\dfrac{28.2}{0.9691}$ = $\dfrac{c}{0.9412}$

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

$\dfrac{a}{Sin A}$ = $\dfrac{b}{Sin B}$ = $\dfrac{c}{Sin C}$

Or, $\dfrac{a}{SinA }$ = $\dfrac{c}{Sin C}$

or,  $\dfrac{16}{Sin A}$ = $\dfrac{12}{Sin 31}$

or,  $\dfrac{16}{Sin A}$ = $\dfrac{12}{0.51}$

Or, $\dfrac{16}{Sin A}$ = 23.52

∴ Sin A = $\dfrac{16}{23.52}$

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,  $\dfrac{b}{Sin B}$ = $\dfrac{c}{Sin C}$

or,  $\dfrac{b}{Sin 106.2}$ = $\dfrac{16}{Sin 31}$

Or, $\dfrac{b}{0.96}$ = $\dfrac{16}{0.51}$

or, b = 31.3×0.96

∴ b = 30.04

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

Answer