Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function of the given angle.
5) Find cosA when a=7 an b=2
6) Find tanA when a=7 and b=6
thank you
Hello again, tangerine. We usually label the sides of a right triangle with the lowercase letters corresponding to their opposite angles (as in my drawing).
So,
5. We know $\displaystyle a$ and $\displaystyle b$, but we'll need to use the Pythagorean theorem to get the hypotenuse:
$\displaystyle \cos A = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac bc = \frac2{\sqrt{7^2 + 2^2}} = \frac2{\sqrt{53}} = \frac{2\sqrt{53}}{53}$
6. $\displaystyle \tan A = \frac{\text{opposite}}{\text{adjacent}} = \frac ab = \frac76$
Really, I didn't know for sure since the problem didn't specify. But as I said before, that is the usual convention: side $\displaystyle a$ goes opposite angle $\displaystyle A$, side $\displaystyle b$ opposite angle $\displaystyle B$, etc., and the hypotenuse is usually $\displaystyle c$.
The right angle is always opposite the longest side (hypoteneuse).
So in this case, the hypoteneuse would be c, right angle would be C.
The other two angles A and B are oppsite sides a and b respectively. The positioning of these two sides is irrelevant because you're basically just flipping or turning the same triangle.