Question

Select the true statement about triangle abc?

Answer 1

$Sin\frac{opposite}{hypotenuse}Cos\frac{adjacent}{hypotenuse} Tan\frac{opposite}{adjacent}$

The hypotenuse is the longest side of the triangle. The opposite side is the side across from a point/angle. The adjacent side is the side next to the point.

At point A, AC is the hypotenuse, BC is the opposite, AB is the adjacent.

cos A = 12/13

A.) sin C = 12/13   This is the answer

B.) sin B, the opposite is 13, and the hypotenuse is 13

C.) tan C = 12/5

D.) cos C = 5/13

Answer 2

ANSWER

The true statement is that,

$\cos(A) = \sin(C)$


EXPLANATION

∆ABC is a right angle triangle, with

$hypotensuse = 13 \: units$

The side adjacent to angle A is
$12 \: \: units$


The cosine ratio is given by
$\cos(A) = \frac{length \: of \: adjacent \: side}{hypotenuse}$


This implies that,

$\cos(A) = \frac{12}{13}$

The length of the side opposite to angle C is
$12 \: units$


The sine ratio is,

$\sin(C) = \frac{length \: of \: opposite \: side}{hypotenuse}$

$\sin(C) = \frac{12}{13}$


We can see that the two ratios are the same therefore,


$\cos(A) = \sin(C)$
The correct answer is option A.