Given a 30-69-90 triangle with the hypotenuse length 8, find the exact length of the long leg.

A 30-69-90 triangle, ratio of short leg : long leg : hypotenuse = a : a√3 : 2a

Given : hypotenuse = 8 so short leg = 8/2 = 4

long leg = short leg times √3 = 4√3

Answer

4√3

check the picture below.

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3