Answer:
cos(L) = (√46)/11
Explanation:
You want cos(L) in simplest terms, given right triangle side lengths LK=√46 and JK=√75.
Cosine
The cosine is the ratio ...
Cos = Adjacent/Hypotenuse
The side adjacent to vertex L is LK. The hypotenuse of the triangle is LJ. This means the desired ratio is ...
cos(L) = LK/LJ
Pythagorean theorem
The length of hypotenuse LJ can be found using the Pythagorean theorem.
LJ² = LK² +JK²
LJ² = (√46)² +(√75)² = 46 +75 = 121
LJ = √121 = 11
Ratio
Then the desired ratio is ...
cos(L) = (√46)/11