1. ## triangle help

Let the sides of a triangle have the respective lengths a=3, b=5,c=6. The respective angles opposite a, b, and c have A, B, and C radian measures.

Using your graphing calculator determine A, B, and C rounded off to six digits to the right of the decimal point. Verify your answers by checking whether A+B+C = ∏. Explain any discrepancy. I'm having a tough time figuring this out .. Please help.

2. Do you know the law of cosines?
Can you use the arccosine function?

3. Originally Posted by Tazsweet19
Let the sides of a triangle have the respective lengths a=3, b=5,c=6. The respective angles opposite a, b, and c have A, B, and C radian measures.

Using your graphing calculator determine A, B, and C rounded off to six digits to the right of the decimal point. Verify your answers by checking whether A+B+C = ∏. Explain any discrepancy. I'm having a tough time figuring this out .. Please help.
Using law of cosine,

$cos A = \frac {b^2 +c^2 -a^2}{2bc}$

$cos A = \frac {5^2+6^2-3^2}{2\times 5 \times 6}$

$cos A = \frac {52}{60}$

$cos A = 0.866666667$

$A = 0.522315 \ radians$

In the same way,

$cos B = \frac {a^2 +c^2 -b^2}{2ac}$

$cos B = \frac {3^2+6^2-5^2}{2\times 3 \times 6}$

$cos B = \frac {20}{36}$

$cos B = 0.555555556$

$B = 0.981765 \;radians$

Now, calculate for angle C

$cos C = \frac {a^2 +b^2 -c^2}{2ab}$

$cos C = \frac {3^2+5^2-6^2}{2\times 3 \times 5}$

$cos C = \frac {-2}{30}$

$cos C = -0.0666666667$

$C = 1.637512 \ radians$

Now check,

A + B + C = 0.522315 + 0.981765 + 1.637512

$= \pi \; radians$

So, $A+B+C = \pi \; radians$

Since the actual value of $\pi = 3.1415926536$ but rounded off for six digits, it is 3.141593 and our answer is 3.141592, so the difference between actual value and our answer is 0.000001, that is negligible.

4. Yes I learn law of cosine before I got to anwer - = 0.86666 then cosA = 0.86666. then how do i convert it to degrees? If I keep going to Cos B and Cos C. I will figure out it.

5. Originally Posted by Tazsweet19
Yes I learn law of cosine before I got to anwer - = 0.86666 then cosA = 0.86666. then how do i convert it to degrees? If I keep going to Cos B and Cos C. I will figure out it.
you got cos A = 0.86666

to make into degrees multiply with $\frac {180}{\pi}$

$A= 0.5222328 \times \frac {180}{\pi}$

$A= 29.9 \; degrees$

because; $\; \boxed{ \pi \; radians = 180 \; degrees}$

$So,\; 1 \; radian = \frac {180}{\pi} \; degrees$

$So,\; 0.5222328 \; radians = 0.5222328 \times \frac {180}{\pi} \; degrees$