Math / Trigonometry

QuestionExploring... $\sin (B)=\frac{\text { opposite }}{\text { hypotenuse }}$ $\cos (B)=\frac{\text { adjacent }}{\text { hypotenuse }}$ $\tan (B)=\frac{\text { opposite }}{\text { adjacent }}$ 1) Which ratio represents $\cos A$ in the accompanying diagram of $\triangle A B C$ ? (1) $\frac{5}{13}$ (3) $\frac{12}{5}$ (2) $\frac{12}{13}$ (4) $\frac{13}{5}$

Studdy Solution

STEP 1

1. We are working with a right triangle $\triangle ABC$ .
2. The side lengths are given as $AC = 5$ , $BC = 12$ , and $AB = 13$ .
3. We need to find the cosine of angle $A$ .

STEP 2

1. Identify the sides relevant to angle $A$ .
2. Recall the definition of cosine.
3. Calculate the cosine of angle $A$ .

STEP 3

Identify the sides relevant to angle $A$ in the triangle. The side $AC$ is adjacent to angle $A$ , $BC$ is opposite to angle $A$ , and $AB$ is the hypotenuse.

STEP 4

Recall the definition of cosine: $\cos(A) = \frac{\text{adjacent side}}{\text{hypotenuse}}$

STEP 5

Substitute the known side lengths into the cosine formula: $\cos(A) = \frac{AC}{AB} = \frac{5}{13}$
The ratio that represents $\cos A$ is:
$\boxed{\frac{5}{13}}$

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