Question

Given that A=84, B=66 and a=13 solve triangle ABC. Round to the nearest hundredth.

Answer 1

To solve triangle ABC, calculate angle C by subtracting angles A and B from 180. Use the Law of Sines with angle A, angle B, and side a to find sides b and c. Round the final answers to the nearest hundredth.

Step-by-step explanation:

To solve triangle ABC, given that angle A = 84 degrees, angle B = 66 degrees, and side a = 13, we start by finding angle C. Since the sum of angles in a triangle equals 180 degrees, angle C can be found as follows:

C = 180 - A - B

C = 180 - 84 - 66

C = 30 degrees

With angle C and side a known, we can now use the Law of Sines to find the other sides, b and c:

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

We will focus on finding side b using:

\(b = \frac{a * \sin B}{\sin A}\)

\(b = \frac{13 * \sin 66}{\sin 84}\)

After calculating this with a calculator, we round the result to the nearest hundredth, as instructed.

Then, we would repeat a similar process to find side c using:

\(c = \frac{a * \sin C}{\sin A}\)

Note that due to rounding, instruction to round results to the nearest hundredth is crucial for precision as shown with the example of 201.867 rounding to 201.87.

Answer 2

In this item, we are asked to determine the sides and the angles of the given triangle ABC. We use the cosine law for the first one,

A/cos A = B/cos B

Substituting,
84 / cos 13° = 66/ cos b
The value of b is equal to 40°.

The sum of the measures of the angle in the triangle is equal to 180°
a + b + c = 180°

13 + 40 + c = 180°

c = 127°

Use again Sine Law,
B/ sinb= C / sin c

Substituting,
66/sin 13 = C/sin .
The value of c from the equation is 127.32.