Question

How do you solve a triangle given <A=84.2°, <B=20.7°, B=17.2?

Answer 1

The following diagram represents your problem

Explanation:

Step 1:

Since we know an angle opposite a known side, we can use the Sine Rule to solve for side a.

`sinA/a = sinB/b = sinC/c`

`sin84.2/a = sin20.7/17.2 = sinC/c`

`a = (17.2 xx sin84.2)/sin20.7`

`a = 48.4`

Step 2:

We could have done this at first, but let's find angle C. We know that the sum of the three angles in a triangle always equals 180. Therefore, we can set up the following equation:

`C + 20.7 + 84.2 = 180`

`C = 180 - 20.7 - 84.2`

`C = 75.1˚`

Step 3:

We must now substitute the value of angle C to find side C.

`SinB/b = sinC/c`

`sin20.7/17.2 = sin75.1/c`

`(17.2 xx sin75.1)/sin20.7 = c`

`47.0 = c`

Summary:

Your triangle has the following dimensions:

`/_A = 84.2˚`
`/_B = 20.7˚`
`/_C = 75.1˚`

`a = 48.4` units
`b = 17.2` units
`c = 47.0` units

Hopefully this helps!