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The triangle ABC is right-angled with a right angle at the corner C. Calculate the area of the triangle if c = |AB| = 10 and tan for B is 1/5.

I take it I have to use the area formula with sin, but I have no idea how... I have tried drawing a triangle, though without success.

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  • $\begingroup$ What does "$C = |AB| = 10$" mean? $\endgroup$ – Zain Patel Jul 13 '16 at 11:45
  • $\begingroup$ Oh, supposed to be a minor c. So the opposite side to the angle C = c and it's 10 units long. $\endgroup$ – user23451 Jul 13 '16 at 11:48
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Suppose $BC = x$, then $AC = 5x$. Now apply Pythagorean Theorem to get the equation and solve it for $x$. Now you know each side of the triangle. Can you proceed?

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  • $\begingroup$ Note that $$\tan B = \frac{|AC|}{|BC|}$$ so you should have $|AC| = x$ and $|BC| = 5x$. $\endgroup$ – N. F. Taussig Jul 13 '16 at 15:09

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