Question

Solve for the remaining angle and sides of the triangle described below. Round to the nearest hundredtheA = 50°. B = 45,a=3

Answer 1

Given:

The angels and sides of the triangle are

A = 50°. B = 45°, and a=3

Aim:

We need to find the angle C and sides c and b.

Step-by-step explanation:

Use sine law.

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

`\text{ Consider }(\sin A)/(a)=(\sin B)/(b)\text{ to find side b.}`

Substitute A = 50°. B = 45°, and a=3 in the equation.

`(\sin 50^o)/(3)=(\sin 45^o)/(b)`

`b=(\sin 45^o)/(\sin 50^o)*3`
`b=2.77`

Use the triangle sum property to find the angle C.

`A+B+C=180^o`

Substitute A = 50°. and B = 45° in the equation.

`50^o+45^o+C=180^o`

`95^o+C=180^o`

`C=180^o-95^o`

`C=85^o`

`\text{ Consider }(\sin A)/(a)=(\sin C)/(c)\text{ to find side c.}`

Substitute A = 50°. C= 85°, and a=3 in the equation.

`(\sin50^o)/(3)=(\sin 85^o)/(c)`

`c=(\sin 85^o)/(\sin 50^o)*3`
`c=3.90`

Final answer:

`C=85^o`
`b=2.77`
`c=3.90`