Question

Solve for the remaining angles and side of the one triangle that can be created. Round to the nearest hundredth:A = 100"a = 3.5, b = 3

Answer 1

Given:

• A = 100 degrees

,

• a = 3.5

,

• b = 3

Let's solve for the remaining angles and side of the triangle.

Here, we are given one angle and two sides.

To solve, apply the Law of Sines:

`(\sin A)/(a)=(\sin B)/(b)=(\sin C)/(c)`

• To solve for measure of angle B, we have:

`\begin{gathered} (\sin A)/(a)=(\sin B)/(b) \\ \\ (\sin100)/(3.5)=(\sin B)/(3) \\ \\ \sin B=(3\sin 100)/(3.5) \\ \\ \sin B=(2.954)/(3.5) \\ \\ \sin B=0.844 \end{gathered}`

Take the sine inverse of both sides:

`\begin{gathered} B=\sin ^(-1)(0.844) \\ \\ B=57.58^0 \end{gathered}`

Therefore, the measue of angle B is = 57.58 degrees.

• To solve for angle C, apply the Triangle Angle Sum Theorem.

m∠A + m∠B + m∠C = 180

m∠C = 180 - m∠A - m∠B

m∠C = 180 - 100 - 57.68

m∠C = 22.32

The measure of angle C is 22.32 degrees.

• To find the length of c, apply the Law of Sines:

`\begin{gathered} (\sin A)/(a)=(\sin C)/(c) \\ \\ (\sin100)/(3.5)=(\sin 22.32)/(c) \\ \\ c=(3.5\sin 22.32)/(\sin 100)\tan ^(-1)\tan ^(-1) \\ \\ c=(1.329)/(0.9848) \\ \\ c=1.35 \end{gathered}`

The length of side c is 1.35 units.

ANSWER:

• B = 57.58,°

,

• C = 22.32,°

,

• c = 1.35