Question

Have to use laws of sines, can someone solve this one?

Answer 1

Answer/Step-by-step explanation:

✔️Find <K using law of sines:

Thus,

`(sin(K))/(k) = (sin(H))/(h)`

K = ??

k = 37 mm

H = 34°

h = 29 mm

Plug in the values

`(sin(K))/(37) = (sin(34))/(29)`

Multiply both sides by 37

`(sin(K))/(37)*37 = (sin(34))/(29)*37`

`sin(K) = (sin(34)*37)/(29)`

`sin(K) = 0.713453014`

`K = sin^(-1)(0.713453014)`

`K = 45.5 degrees` (nearest tenth)

✔️Find J:

m<J = 180° - (45.5° + 34°) (sum of ∆)

m<J = 100.5°

✔️Find j using Sine rule:

`(j)/(sin(J)) = (h)/(sin(H))`

J = 100.5°

j = ??

H = 34°

h = 29 mm

Plug in the values

`(j)/(sin(100.5)) = (29)/(sin(34))`

Multiply both sides by sin(100.5)

`(j)/(sin(100.5))*sin(100.5) = (29)/(sin(34))*sin(100.5)`

`j = (29*sin(100.5))/(sin(34))`

j = 51.0 mm (nearest tenth)