triangle help

**Tazsweet19** · September 6th 2008, 09:42 AM

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.

**Plato** · September 6th 2008, 10:04 AM

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

**Shyam** · September 6th 2008, 11:28 AM

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

= 3.141592 radians

$= \pi \; radians$

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.

**Tazsweet19** · September 6th 2008, 11:36 AM

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.

**Shyam** · September 6th 2008, 06:48 PM

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

A= 0.5222328 radians

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

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

$A= 29.9 \; degrees$

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

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

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

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