Verified answer

If you can picture a ladder leaning against a building, it will form a right triangle:

............../

............/..|

.12..../.....| Building

...../.........|

../............|

---------------

........x

...horrible drawing, but hopefully you can see it. the angle on the left is 75°. Since the triangle is a right triangle, the angle on the right is 90°, which leaves 15° for the top angle.

You're solving for x, so you'd need a function that would include x in the computation. You could use sine or cosine depending on which angle you chose.

sin (15) = x / 12

or

cos (75) = x / 12

For either one, you'd calculate the function, and then multiply that answer by 12 (to get x by itself), and you'll have the answer

cos (75) = x / 12

0.2588 = x / 12

3.1058 = x

So x = 3.1058 ft, the distance from the bottom of the ladder to the building.

The ladder, the ground between the wall and the base of the ladder, and the wall from the ground to the top of the ladder form a right triangle.

The ladder is the hypotenuse,

the ground between the wall and the base of the ladder is the adjacent side,

and the wall from the ground to the top of the ladder is the opposite side of the right triangle.

The ratio of the measure of the ground between the wall and the base of the ladder (let us call that m) AND the measure of the ladder is equal to the COSINE of the 75 degree angle. The ratio of the measure of the adjacent side to the measure of the hypotenuse is the COSINE of the angle between those two sides of the right triangle.

m / 12 = cos 75

m = 12cos 75

m = 12(0.2588)

m = 3.1 ft

cos75= x/12

x=3.1058 ft.