ladder 6.5m long at angle of 50degrees how high up wall does ladder reach

If the 50° refers to the angle between the ladder and the ground then you have a right angled triangle for which you know the angle and hypotenuse and want to find the "opposite", so you have:

 

sin(50°) = opposite/hypotenuse or opposite = hypotenuse*sin(50°) so opposite = 6.5*sin(50°) m

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