Answer:
[tex] cos A = \frac{5}{13} [/tex]
Step-by-step explanation:
The given triangle, ∆ABC is a right triangle.
To find cos A, we'd need to apply the trigonometric ratio formula, which is cos A = adjacent length/hypotenuse length
From the ∆ given,
AC = adjacent = 15,
BC = opposite = 36
We are not given the hypotenuse length AB.
==>Find the hypotenuse length AB, using the Pythagorean theorem formula:
c² = a² + b²
AB² = 15² + 36² = 225 + 1296 = 1521
AB = √1521
AB = 39
==>Find cos A:
cos A = adjacent/hypotenuse
[tex] cos A = \frac{adjacent}{hypotenuse} [/tex]
Adjacent = AC = 15
Hypotenuse = AB = 39
[tex] cos A = \frac{15}{39} [/tex]
[tex] cos A = \frac{5}{13} [/tex]
