Ladder question

Question

A ladder leans again a vertical wall. If the ladder reaches 12 ft up the wall and the foot of the ladder is 5 ft from the wall, determine the angle that the ladder makes with the wall and the length of the ladder. Include a diagram.

Answer 1

length of ladder : a² + b² = c²

122+52=c2

144+25=c²

169=c²

13=c

The ladder is 13ft long.

angle that the ladder makes with wall : tan 5/12 = 22.25°