Question

Someone please help meeeeeee

Answer 1

Answer:

Step-by-step explanation:

Sine rule of Law of sine:

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

Side 'a' faces ∠A.

Side 'b' faces ∠B.

Side 'c' faces ∠C.

We have to find ∠C using angle sum property of triangle.

  ∠C + 75 + 42 = 180

         ∠C +117   = 180

                  ∠C  = 180 - 117

                 ∠C = 63°

$\sf \dfrac{a}{Sin \ 42}= \dfrac{22}{Sin \ 63}\\\\ \dfrac{a}{0.67}=\dfrac{22}{0.89}$

   $\sf a = \dfrac{22}{0.89}*0.67\\\\ \boxed{a = 16.56 \ cm }$

                        $\sf \dfrac{b}{Sin \ B} = \dfrac{c}{Sin \ C}\\\\ \dfrac{b}{Sin \ 75}=\dfrac{22}{Sin 63}\\\\ \dfrac{b}{0.97} =\dfrac{22}{0.89}$

                             $\sf b = \dfrac{22}{0.89}*0.97\\\\ \boxed{b =23.98 \ cm }$

                       

Answer 2

Answer:

a ≈ 16.5 cm , b ≈ 23.8 cm

Step-by-step explanation:

using the Law of Sines in Δ ABC

$\frac{a}{sinA}$ = $\frac{b}{sinB}$ = $\frac{c}{sinC}$

we require to calculate ∠ C

∠ C = 180° - (42 + 75)° = 180° - 117° = 63°

Then to find a

$\frac{a}{sinA}$ = $\frac{c}{sinC}$ ( substitute values )

$\frac{a}{sin42}$ = $\frac{22}{sin63}$ ( cross- multiply )

a × sin63° = 22 × sin42° ( divide both sides by sin63° )

a = $\frac{22sin42}{sin63}$ ≈ 16.5 cm ( to the nearest tenth )

similarly to find b

$\frac{b}{sinB}$ = $\frac{c}{sinC}$ ( substitute values )

$\frac{b}{sin75}$ = $\frac{22}{sin63}$ ( cross- multiply )

b × sin63° = 22 × sin75° ( divide both sides by sin63° )

b = $\frac{22sin75}{sin63}$ ≈ 23.8 cm ( to the nearest tenth )