A25-foot ladder is leaning against a house with the base of the ladder 5 feet from the house. how high up the house does the ladder reach? if necessary, round to the nearest tenth foot.

  24.5 ft

Step-by-step explanation:

The Pythagorean theorem relates the lengths of the legs of a right triangle to the length of the hypotenuse. This geometry is modeled by a right triangle with one leg being 5 ft and the hypotenuse being 25 ft. Then we have (in feet), ...

  25^2 = 5^2 + height^2

  625 -25 = height^2 . . . . . . subtract 5^2

  √600 = height ≈ 24.4949 . . . . take the square root

The ladder reaches about 24.5 ft up the house.

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,