Question

Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles.

C = 67°, a = 21, c = 20


Help please show work please

Answer 1

Answer on Question #42399 – Math – Geometry

Question:

Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles.

$$C = 67{}^{\circ}, a = 21, c = 20.$$

Answer:

The Law of Sines is very useful for solving triangles:

$$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$

where $a$, $b$ and $c$ are sides; $A$, $B$, $C$ are angles.

$$\frac{21}{\sin A} = \frac{b}{\sin B} = \frac{20}{\sin 67{}^{\circ}}$$

Then

$$\sin A = \frac{21 \times \sin 67{}^{\circ}}{20} = 0.967 \approx 0.97$$ $$A = \arc(\sin(0.97)) = 75.93{}^{\circ} \approx 76{}^{\circ}$$

Now we can calculate angel B. As you know in a triangle, the three angles always add to $180{}^{\circ}$.

$$A + B + C = 180$$ $$76{}^{\circ} + B + 67{}^{\circ} = 180{}^{\circ}$$ $$B = 37{}^{\circ}.$$

Then

$$\frac{b}{\sin 37{}^{\circ}} = \frac{20}{\sin 67{}^{\circ}}$$ $$b = \frac{20 \times \sin 37{}^{\circ}}{\sin 67{}^{\circ}} = 13.1 \approx 13$$

Answer:

$$b = 13; A = 76{}^{\circ}; B = 37{}^{\circ}.$$

www.AssignmentExpert.com