# Homework Help: Measure of the smallest angle in the triangle

1. Aug 16, 2010

### priscilla98

1. The problem statement, all variables and given/known data

In a triangle, two sides that measure 6 centimeters and 10 centimeters form an angle that measures 80 degrees. Find to the nearest degree, the measure of the smallest angle in the triangle.

2. Relevant equations

A2 = B2 + C2 – 2bc Cos A

3. The attempt at a solution

I tried using this formula to get the answer but it didn't work out. This is one of the questions from the algebra 2 trigonometry regents. I know the answer which is 33 degrees but I dont know on how to get to that answer.

2. Aug 16, 2010

### praharmitra

Re: Trigonometry

I think relevant equation would actually be

$$\frac{a}{sinA} = \frac{b}{sinB} = \frac{c}{sinC}$$

along with the equation you've mentioned

3. Aug 16, 2010

### priscilla98

Re: Trigonometry

Okay, then a = 6, b = 10 and C = 80 degrees, right? Then idk how to use the revelant equations you implied.

4. Aug 16, 2010

### praharmitra

Re: Trigonometry

i just edited my reply. use your equation first and find c. Then use my equation to get A and B

5. Aug 16, 2010

### eumyang

Re: Trigonometry

Can you show us your work? Because I was able to get the answer (approx 33.409°). Make sure you are in degree mode when doing your calculations (or convert the 80° to radians).

Perhaps using the Law of Sines will work, but the OP may be required to use Law of Cosines for this problem.

69

EDIT: Too slow ^.^

6. Aug 16, 2010

### priscilla98

Re: Trigonometry

Thanks a lot praharmitra for this. I really appreciate it.

7. Aug 16, 2010

### CompuChip

Re: Trigonometry

Actually, if you're not sure about the sine law, you can solve it using sin, cos and tan in right-angled triangles (draw the triangle, call its height h and relate it to the sine of 80 degrees, then divide the side of length 10 into two pieces of length L and 10 - L and relate L to the cosine of 80 degrees).

8. Aug 16, 2010

### Willian93

Re: Trigonometry

first you need to find side c using cosine law c2=a2 +b2=2abcosC
then use sine law to find angle A, cause the higher angle, the longer the side, since side A is the shortest, which means angle A is the smallest.