Before finding the values of all trigonometric functions, fidn the length of the segment LM, by using the Pithagorean theorem, as follow:
(LN)² = (MN)² + (LM)²
MN = 6
LN = 10
solve the equation for LM and replace the values of the other parameters:
(LM)² = (LN)² - (MN)²
(LM)² = (10)² - (6)²
(LM)² = 100 - 36
(LM)² = 64
LM = √64
LM = 8
Take into account that:
cos x = adjacent side to x / hypotenuse
sin x = opposit side to x/ hypotenuse
tan x = opposite side to x / adjacent side to x
Next, find the value of the required functions:
1. sin L = MN/LN = 6/10 = 3/5
2. tan L = MN/LM = 6/8 = 3/4
3. cos L = LM/LN = 8/10 = 4/5
4. sin N = LM/LN = 8/10 = 4/5