A 12 foot ladder is leaning up against the side of a house the ladder makes an angle of 62° with the ground. How far up the side of the house does the ladder reach?

Step-by-step explanation:

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

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

To determine the height, h that the ladder reaches, we would apply

the Sine trigonometric ratio.

Sin θ = opposite side/hypotenuse. Therefore,

Sin 62 = h/12

h = 12Sin62

h = 12 * 0.8829

h = 10.6 feet