A ladder is leaning against the side of a house and forms a 65 degree Angel with the ground. The foot of the ladder is 8 feet from the house. Find the length of the ladder

the length of the ladder is 8.827ft

Step-by-step explanation:

We know that the angle formed between the floor and the stairs is 65 °

the height at which the ladder reaches is 8 feet

between the floor and the house we know that we have a 90 degree angle

so we have a right triangle with its 8 foot wall leg

and an angle of 65 degrees on the floor and the stairs

the length of the stairs in this triangle would represent the hypotenuse

we have the angle and measure of the opposite leg, we want to know the hypotenuse

it is known that the sine of an angle in a rectangular triangle is equal to the opposite leg on the hypotenuse

sin 65° = op / hyp

sin 65° = 8 / hyp

0.9063 = 8 / hyp

hyp = 8 / 0.9063

hyp = 8.827