Answer:
tan∅ = 3√29/10
Step-by-step explanation:
Pythagorean Theorem: a² + b² = c²
cos∅ = adjacent/hypotenuse
Since we are given cos∅ = 10/19, we know that one leg is 10 and the hypotenuse is 19. We need to find the missing leg length:
10² + b² = 19²
b² = 19² - 10²
b = √261
b = 3√29
We know that tan∅ equals opposite over adjacent. Our adjacent is given to us by cos∅, so we simply plug in our values:
tan∅ = opposite/adjacent
tan∅ = 3√29/10
