Question

Find the missing side or angle.Round to the nearest tenth.A=60°b=50C=48a=[ ? ]

Answer 1

Using this drawing as a guide, the problem becomes easier to tackle. In every triangle, the sum of all 3 angles must be equal to 180 degrees. You have no way of knowing the angle that would be B, so a good strategy is to cut a line just below the angle C so you get 2 right triangles.

Then, using the sine law, you can use that sin(A)=a'/b, where a' is not a but the right side of the new triangle.

By using the previous formula, you get that b*sin(A)=a'=50*sin(60 degrees)=43.3. You also have that cos(A)=(c-x)/b so -cos(A)*b +c=x

`x=-\cos (60^(\circ))\cdot50\text{ +48 =}23`

So, with a' and x, you can apply the Pythagorean theorem to find a.

`a^(\prime2)+x^2=a^2\rightarrow a=\sqrt[]{23^2+43.3^2}=49.0`

This is the length a, which is the final answer.