number 8 how tall is the peak of the ceiling

Question

you have just moved into a new house, and your bedroom is in the attic. the ceiling of the attic is slanted and reaches a peak over the middle of the floor. you want to know how high that peak is. beginning directly under the peak you measure 17 feet to the corner where the ceiling meets the floorboards. also you know that your dresser is 4 feet 6 inches tall. you push it against the wall as far as it will go, and you measure the remaining distance between the back of the dresser and the corner where the ceiling meets the floorboards. this distance is 3.5 feet, how tall is the peak of the ceiling

Answer 1

the height of the peak, the 17' distance and the slope of the ceiling form a right triangle

when you push the dresser up against the wall as far as it will go you form another right triangle similar to the previous one

the legs of the large triangle are h, the height of the ceiling, and the 17' distance

the legs of the small triangle are 4.5' and 3.5 '

4.5 corresponds to h and 3.5 corresponds to 17

4.5/h=3.5/17

cross multiply

3.5*h=4.5*17

3.5h=76.5

h=76.5/3.5

h=21.857 feet is the height of the ceiling