Question

In the pic.............

Answer 1

Given -

a = 2.5 cm

b = 3.6 cm

∠A = 43°

To Find -

Remaining angles and sides =?

Step-by-Step Explanation -

We will start by drawing the diagram:

Now, we know

By, sine rule:

`\begin{gathered} (\sin A)/(a)\text{ =}(\sin B)/(b)=(\sin C)/(c) \\ \\ =\text{ }(\sin43)/(2.5)\text{ = }(\sin C)/(3.6) \\ \\ =\text{ }\sin C\text{ = }(3.6*\sin44)/(2.5) \\ \\ =\text{ }\sin C\text{ = 0.9820} \\ \\ C\text{ = }\sin^(-1)(0.9820) \\ \\ C\text{ = 79} \\ \end{gathered}`

Now, we know N

A + B + C = 180 c°°

43 + B + 79° = 180°°

B = 180° - 799 - 43°°

B = 58°

Now, Side b =

`\begin{gathered} (\sin A)/(a)\text{ = }(\sin B)/(b) \\ \\ (\sin43)/(2.5)\text{ = }(\sin58°)/(b) \\ \\ b\text{ = }(2.5*\sin58°)/(\sin43°) \\ \\ b\text{ = 3.1} \end{gathered}`

Final Answer -

∠B = 58B°

∠C = 797°

Side, b = 3.1 cm