Help, with area and perimeter of triangle please!

**gobbajeezalus** · October 9th 2008, 10:43 AM

Please show work, thanks a ton!

**jaydee323** · October 9th 2008, 11:29 AM

Hint:

Use Sine Rule

a/sinA = b/sinB = c/sinC

to find missing lengths & angles.

Use Area = 1/2abSinC to calculate the area

**masters** · October 9th 2008, 11:46 AM

Use law of sines to find angle B. See diagram.

$\frac{\sin 15}{8}=\frac{\sin B}{11}$

$\sin B=\frac{11 \sin 15}{8} \approx .3559$

$\sin^{-1}=20.8^{\circ}$

$\angle C=144.2^{\circ}$

Now, use the law of sin again to find the missing side c.

$\frac{\sin 15}{8}=\frac{\sin 144.2}{c}$

Once you find c using the formula above, you will have all the sides needed.

P = a + b + c

Use Heron's formula to find the area:

$A=\sqrt{s(s-a)(s-b)(s-c)}$ where $s=\frac{a+b+c}{2}$

**gobbajeezalus** · October 11th 2008, 09:18 AM

Originally Posted by masters

Use law of sines to find angle B. See diagram.

$\frac{\sin 15}{8}=\frac{\sin B}{11}$

$\sin B=\frac{11 \sin 15}{8} \approx .3559$

$\sin^{-1}=20.8^{\circ}$

$\angle C=144.2^{\circ}$

Now, use the law of sin again to find the missing side c.

$\frac{\sin 15}{8}=\frac{\sin 144.2}{c}$

Once you find c using the formula above, you will have all the sides needed.

P = a + b + c

Use Heron's formula to find the area:

$A=\sqrt{s(s-a)(s-b)(s-c)}$ where $s=\frac{a+b+c}{2}$

Hi,

everything makes perfect sense so far EXCEPT for the last part that I bolded. Can someone please help me on this heron's formula and tell me the area of this triangle with work?

Thanks a ton!!!!

**masters** · October 11th 2008, 02:34 PM

Originally Posted by gobbajeezalus

Hi,

everything makes perfect sense so far EXCEPT for the last part that I bolded. Can someone please help me on this heron's formula and tell me the area of this triangle with work?

Thanks a ton!!!!

Heron's formula is used to find the area of a triangle when only the sides are known. It's pretty straight forward.

The sides are represented as: a, b, and c.

s stands for half the periimeter.

If you follow all the steps that have been given to you, you will have the lengths of the three sides.

After that, it's just plug and chug.

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