Answer/Step-by-step explanation:
✔️Find <K using law of sines:
Thus,
[tex] \frac{sin(K)}{k} = \frac{sin(H)}{h} [/tex]
K = ??
k = 37 mm
H = 34°
h = 29 mm
Plug in the values
[tex] \frac{sin(K)}{37} = \frac{sin(34)}{29} [/tex]
Multiply both sides by 37
[tex] \frac{sin(K)}{37}*37 = \frac{sin(34)}{29}*37 [/tex]
[tex] sin(K) = \frac{sin(34)*37}{29} [/tex]
[tex] sin(K) = 0.713453014 [/tex]
[tex] K = sin^{-1}(0.713453014) [/tex]
[tex] K = 45.5 degrees [/tex] (nearest tenth)
✔️Find J:
m<J = 180° - (45.5° + 34°) (sum of ∆)
m<J = 100.5°
✔️Find j using Sine rule:
[tex] \frac{j}{sin(J)} = \frac{h}{sin(H)} [/tex]
J = 100.5°
j = ??
H = 34°
h = 29 mm
Plug in the values
[tex] \frac{j}{sin(100.5)} = \frac{29}{sin(34)} [/tex]
Multiply both sides by sin(100.5)
[tex] \frac{j}{sin(100.5)}*sin(100.5) = \frac{29}{sin(34)}*sin(100.5) [/tex]
[tex] j = \frac{29*sin(100.5)}{sin(34)} [/tex]
j = 51.0 mm (nearest tenth)
