Question

Find the exact values of sin A and cos A. Write fractions in lowest terms. (5 points) A right triangle ABC is shown. Leg AC has length 33, leg BC has length 44, and hypotenuse AB has length 55.
sin A = four fifths ; cos A = three fifths
sin A = three fifths ; cos A = four fifths
sin A = five fourths ; cos A = five thirds
sin A = four thirds ; cos A = three fourths

Answer 1

$sin\ A = \frac{4}{5}\\\\cos\ A = \frac{3}{5}$

Solution:

Given a right triangle ABC

The figure is attached below

From given,

AC = Base = 33

BC = Perpendicular = 44

AB = hyptotenuse = 55

We know that,

$Sin\ A = \frac{perpendicular}{hypotenuse}\\\\Sin\ A = \frac{44}{55}\\\\Sin\ A = \frac{4}{5}$

Also,

$cos\ A = \frac{base}{hypotenuse}\\\\cos\ A = \frac{33}{55}\\\\cos\ A = \frac{3}{5}$

Thus the values are found