Problem Question

Question

Amber wants to see the village on the other side of a 9-foot wall. She can do this if she will place a 7-foot ladder such that the top of the ladder is 6 ft. high up the wall.

a) If she is to achieve this, how far from the wall should the foot of the ladder be?

b) What is the measure in degrees of the angle that the wall makes with the ladder?

Answer 1

7^2 = 6^2 + b^2 the ladder, wall and ground form a right triangle. the ladder is the hypotenuse which squared = sum of the other two sides, each squared.

49 = 36 + b^2

b^2 = 49-36 = 13

b = sqr13 = about 3.61 feet from bottom of the ladder to the wall or about 3 feet and 7 1/3 inches

angle =sin^-1(6/7) = close to 59 degrees

if it had been 60 degrees, it would have been a 1-sqr3-2 ratio right triangle and a hypotenuse of 7 would mean a base of 1/2 of 7 or 3.5 feet. 59 degrees is slightly less than 60, so the base is slightly more than 3.5 feet.