Answer:
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
