Using Tan to find the area of a triangle

I have come across a question that I can't seem to figure out.

If tanA = 3/4, find the area of the given triangle without using a calculator

The given triangle is an scalene triangle with a side of 8cm and 7cm with angle A in between both sides.

I am not really too sure how to do this without a calculator. Normally, I would have followed through with absinC. I think I may be going in the wrong direction though. I am at a loss for what to do with this question.

Any help would be appreciated to steer me in the right direction.

• hint: draw a diagram – John Joy Aug 19 '15 at 16:46

1 Answer

HINT

I would say, if $\tan \alpha = \frac{3}{4}$ then $\sin \alpha = \frac{3}{5}$

It simply find from a right triangle with sides 3, 4, 5.

• I considered that when I was trying the question myself. But I do not know how to relate the right angled triangle with sides 3, 4 and 5 to the scalene triangle with sides 7 and 8. – Roy Sheehan Aug 19 '15 at 11:18
• @RoySheehan The right angled triangle with sides 3, 4 and 5 is just a simply tool for conversion $\tan \alpha$ to $\sin \alpha$. – georg Aug 19 '15 at 11:32
• Thank you very much. I don't know how to apply sin for the area as I am unable to use a calculator to solve this task. Any hints you could help me out with? – Roy Sheehan Aug 19 '15 at 11:58
• @RoySheehan Your sentence "The given triangle is an scalene triangle with a side of 8cm and 7cm with angle A in between both sides" I understand that the angle A is the angle between the sides of 8cm and 7cm. Then the area of triangle = $\frac{7\cdot 8}{2}\cdot \sin A=\frac{7\cdot 8}{2}\cdot \frac{3}{5}$, and it can be calculated without using a calculator. If I understood wrong, I apologize. – georg Aug 20 '15 at 7:43