Question

Solve the triangle . a = 12 , b = 22 , C = 95 degrees

Answer 1

Step 1:

Apply cosine and sine rules

`\begin{gathered} Sin\text{e rule} \\ (a)/(\sin A)\text{ = }(b)/(\sin B)\text{ = }(c)/(\sin C) \\ Co\sin e\text{ rule} \\ c^2=a^2+b^2-2ab\text{ }*\text{ cosC} \end{gathered}`

Step 2;

Use the cosine rule to find side c

a = 12, b = 22 , m

`\begin{gathered} c^2=12^2+22^2\text{ - 2}*12*22\text{ }*\text{ cos95} \\ c^2\text{ = 144 + 484 - 528}*(-0.087) \\ c^2\text{ = 673.936} \\ c\text{ = }\sqrt[\square]{673.936} \\ c\text{ = 25.96 } \\ \text{c = 26} \end{gathered}`

Step 3:

Find angle A and B using the sine rule.

`\begin{gathered} (a)/(\sin A)\text{ = }\frac{c}{s\text{inC}} \\ (12)/(\sin A)\text{ = }\frac{26}{s\text{in95}} \\ \sin A\text{ = }\frac{12\text{ }*\text{ sin95}}{26} \\ \sin A\text{ = }\frac{12\text{ }*\text{ 0.99619}}{26} \\ \sin A\text{ = 0.4597821684} \\ A=sin^(-1)(0.4597821684) \\ A\text{ = 27.4} \\ A\text{ }\approx\text{ 27}.6\text{ } \end{gathered}`

Final part

Apply sum of angles in a triangle

A + B + C = 180

27.6 + B + 95 = 180

B = 180 - 95 - 27.6

B = 57.4

Final answer

c = 26 , A = 27.6 , B = 57.4 First option is the correct answer