Question

use △abc to determine the ratios for each trigonometric function of ∠a.
a
12
b
13
5
c
sin a = select
select
cos a = 5/13
5/12
tan a = 12/13

Explanation:

Step1: Recall trigonometric ratios

For a right triangle, the sine of an angle is the ratio of the length of the opposite side to the hypotenuse, cosine is the ratio of the adjacent side to the hypotenuse, and tangent is the ratio of the opposite side to the adjacent side.

In $\triangle ABC$ with right angle at $B$, for $\angle A$:

• Opposite side to $\angle A$: $BC = 5$
• Adjacent side to $\angle A$: $AB = 12$
• Hypotenuse: $AC = 13$

Step2: Calculate $\sin A$

$\sin A=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{BC}{AC}=\frac{5}{13}$

Step3: Calculate $\cos A$

$\cos A=\frac{\text{adjacent}}{\text{hypotenuse}}=\frac{AB}{AC}=\frac{12}{13}$

Step4: Calculate $\tan A$

$\tan A=\frac{\text{opposite}}{\text{adjacent}}=\frac{BC}{AB}=\frac{5}{12}$

Answer:

s:
$\sin A = \boldsymbol{\frac{5}{13}}$
$\cos A = \boldsymbol{\frac{12}{13}}$
$\tan A = \boldsymbol{\frac{5}{12}}$