Question

In ΔABC, which trigonometric ratio has the value a/c

Answer 1

Answer:

$\tan A$

Step-by-step explanation:

From the diagram, side length $a$ is opposite to angle A and side length $c$ is adjacent  to angle A.

Recall the mnemonics SOH CAH TOA.

We use TOA, because it involves opposite and adjacent.

$\tan A=\frac{Opposite}{Adjacent}$

$\tan A=\frac{a}{c}$

The correct choice is A.

Answer 2

Hello!

The answer is:  A. Tan(A)

Why?

Since it's a right triangle, we must remember the following trigonometric identities:

$sin\alpha =\frac{opposite}{hypotenuse}\\\\cos\alpha =\frac{adjacent}{hypotenuse}\\\\tan\alpha=\frac{opposite}{adjacent}$

We are going to work with the tangent indentity, so:

If we are looking which a trigonometric ratio/relation which is equal to:

$\frac{a}{c}$

Also, from the image we can see that:

$opposite=a\\adjacent=c\\hypotenuse=b$

So, using the tangent identity, which is equal to:

$tan(A)=\frac{opposite}{adjacent}=\frac{a}{c}$

So, the correct option is A. Tan(A)

Have a nice day!