A ladder is to be placed against a building at a point 15 meters above the ground. The angle of elevation must be 40°. What should the length of the ladder be?

The ladder forms a right angle triangle with the building and the ground. The length of the ladder represents the hypotenuse of the right angle triangle. The height from the top of the ladder to the base of the building represents the opposite side of the right angle triangle.

The distance from the bottom of the ladder to the base of the building represents the adjacent side of the right angle triangle.

To determine the length of the ladder h, The ladder forms a right angle triangle with the building and the ground. The length of the ladder represents the hypotenuse of the right angle triangle. The height from the top of the ladder to the base of the building represents the opposite side of the right angle triangle.

The distance from the bottom of the ladder to the base of the building represents the adjacent side of the right angle triangle.

To determine the length of the ladder h, we would apply

the sine trigonometric ratio.

Sin θ, = opposite side/hypotenuse. Therefore,

Sin 40 = 15/h

h = 15/Sin40 = 15/0.6428

h = 23.3 meters