Question

A 12 foot ladder leans against a building. The angle of elevation from the ground to the foot of the ladder is 46°. Find, to the nearest tenth of a foot, how far is the foot of the ladder from the building

Answer 1

Answer:

8.3 ft

Step-by-step explanation:

Hypotenuse is the longest side

Opposite is the side opposite the angle

Adjacent is the remaining side

Draw the triangle out, and you'll find that the hypotenuse (length of ladder) is 12ft, and that you are looking for the adjacent side (length of the foot of the ladder to the building). Rule out the opposite side (side of building) as it is not needed. The appropriate trigonometric formula is then the $cos(angle) = \frac{adjacent}{hypotenuse}$, rearranged to find the adjacent side is $adjacent = cos(angle)*hypotenuse$  

substitute the values in and you get cos(46) x 12 = 8.335900446