Question

Please help me solve for m<C and m<D​

Answer 1

Explanation:

Use law of cosine to calculate the other side.

c² = a² + b² -2ab Cos C

Here, c is the length of the side which is opposite side to ∠E

a = 29 ; b = 25 and C = 109

c² = 29² + 25² - 2*29*25*Cos 107

= 841 + 625 - 1450* (-0.2923)

= 1466 + 423.835

= 1889.835

c =√1889.835

c = 43.47 ≈ 43

No, find ∠D using again use law of cosine

`Cos \ \beta = \dfra{a^(2)+c^(2)}-b^(2){2ac}\\\\\\ = (29^(2)+43^(2)-25^(2))/(2*29*43)\\\\\\Cos \ \beta =(841+1849-625)/(2494)=(2065)/(2494)\\\\Cos \ \beta = 0.828\\\\\beta =Cos^(-1) \ 0.828\\\\`

β = ∠C = 34°

α = 180 - (34 +107)

α = ∠D = 39

Other angles are

∠C = 34° and ∠D°39