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Area of an oblique triangle question

Hello,

I need help with this question:

"There is a triangle OAB. The length of AO is 10m and AOB has an angle of 0.8^{c}. This triangle also has an arc between points A and B."

**Find the area of the triangle OAB**

Find the area of the sector OAB

I have drawn the triangle to its correct description, see the attached image.

I have tried using the formula for the area of the sector 0.5r^{2}θ, but I got the answer to be 2193. This might be right, just seemed too big. But I do not know the formula for the area of the triangle! (I suppose this triangle is different to the formula 0.5xbxh)

Could you please help me work out how to find the area of this triangle?

Thanks in advance

Dan

Re: Area of an oblique triangle question

Quote:

Originally Posted by

**Danthemaths** Hello,

I need help with this question:

"There is a triangle OAB. The length of AO is 10m and AOB has an angle of 0.8^{c}. This triangle also has an arc between points A and B."

**Find the area of the triangle OAB**

Find the area of the sector OAB

I have drawn the triangle to its correct description, see the attached image.

This webpage will help you.

I cannot help you because I have no idea what $\displaystyle 0.8^c$ could mean.

Re: Area of an oblique triangle question

Quote:

Originally Posted by

**Plato** This webpage will help you.

I cannot help you because I have no idea what $\displaystyle 0.8^c$ could mean.

It means 0.8 radians... C is the symbol for radians, it stands for "number of lengths of the radius on the Circumference".

I suppose we're assuming that it's a circular arc, which means OB = OA, correct?

Re: Area of an oblique triangle question

Yes OB=OA. And 0.8 radians = 57.3 degrees

Re: Area of an oblique triangle question

If the angle is measured in radians, the area of the triangle can be found using $\displaystyle \displaystyle \begin{align*} A = \frac{1}{2}ab\sin{(C)} \end{align*}$ and the area of a sector can be found using $\displaystyle \displaystyle \begin{align*} A = \frac{1}{2}r^2\theta \end{align*}$.