Angle MLK= 66
Hypotenuse (side ML) = 8.757
Side LK = 3.561
First, find the missing angle
A triangles angles add up to 180 so you can do 180-24-90 to get 66.
Next find the side opposite the angle 24. You can use the ratio Tangent (opposite side / adjacent side) and the angle 24.
so Tan (24) = x/8
Cross multiplying will get you Tan(24)* 8 = x
enter this in a calculator and it’s 3.561 (and you can round)
You can now find the hypotenuse, the diagonal side. Use the ratio Sine (opposite side / hypotenuse) and the angle 66.
Sin(66)= 8/x
so x*Sin(66) = 8
divide both sides by sin(66)
x= 8/sin(66)
x= 8.757090228
The hypotenuse is around 8.8