Use the given information to find the lengths of the other two sides of the right triangle if side a is opposite angle a, side b is opposite angle b, and side c is the hypotenuse. cos(b) = 4/5, a = 8

SOH CAH TOA tells you

... cos(B) = a/c

... 4/5 = 8/c

... c = 10 . . . . . multiply by 5c/4

By the Pythagorean theorem,

... b = √c² -a²) = √(10² -8²) = √36 = 6

The lengths of the other two sides are: b = 6, c = 10.

You can tell from the value of the cosine that this is a 3-4-5 right triangle. You can tell from the value of "a" that the scale factor is 2. That means the other two sides are 6 and 10.

use substitution to solve each system of equations. y = x + 5 3x + y = 25 62/87,21 y = x + 5 3x + y = 25 substitute x + 5 for y in the second equation. substitute the solution for x into either equation to find y. the solution is (5, 10)

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