Question

The figure below shows the cross section of the scale model of a roof of a house.

PQR is a right triangle with the right angle at R. RS is the altitude that connects R to PQ. The length of SQ is 4 inches, and the length of PQ is 16 inches.

What is the length of the height RS of the roof rounded to the nearest tenth?

4.5 inches

8.9 inches

2.8 inches

6.9 inches

Answer 1

first find PS

Answer 2

@psi9epsilon How??

Answer 3

ps= pq-sq

Answer 4

@psi9epsilon 12

Answer 5

then try to write an equation in terms of PR^2, USING PYTHAGORAN

Answer 6

PR^2=RS^2+PS^2
also 16^2-QR^2=PR^2=RS^2+PS^2
16^2-(RS^2+SQ^2)=RS^2+PS^2
256-RS^2-16=RS^2+144
96=2RS^2
RS=SQRT(48)=\[4\sqrt{3}\]

Answer 7

Does that help

Answer 8

@psi9epsilon Ohhh!! Okay I see it now. Thank you so much, I had no idea how to do it. That helps a lot, I appreciate it!

Answer 9

let me know if you have doubts, make sure you follow the steps