Question

A ladder leans against a wall making an angle of 60° with ground of the foot of the ladder is 5 meters away from the wall calculate the length of the ladder.

Answer 1

cos $\alpha$ = base/hyp
cos 60 = 5 / x
x = 5/ 0.5
x = 10

Answer 2

imagine a right angled triangle where the perpendicular is representing the wall mentioned in the problem, the hypotenuse representing the ladder and the base of the triangle representing the distance between foot of ladder and the base of the wall.

you already know the value of the base of the triangle which is 5.
you also know the angle between the base and hypotenuse. Simply find the cos of that angle, which is cos60.
so, cos60=base/hypotenuse
ie, 0.5=5/hypotenuse
ie, hypotenuse = 5/0.5
ie, hypotenuse = 10
thus, the length of the ladder is 10metres.