A tightrope walker attaches a cable to the roofs of two adjacent buildings. The cable is 23.5 m long. The angle of inclination of the cable is 13 degrees. The shorter building is 12.0 m high. What is the height of the taller building to the nearest tenth of a metre?

Question

I tried drawing it but it didn't work. I don't which sides to label please help :(

Answer 1

the diagram looks rather routine
draw the smaller building and mark is as 12 m high
draw the other building a bit taller .
draw a horizontal from the smaller to the taller, label the difference in height as x
draw in your cable,
Don't you have a right-angled triangle with a base angle of 13°, opposite as x and hypotenuse as 23.5 M ?

so sin 13° = x/23.5
x = 23.5sin13
= 5.2863..
= 5 m to the nearest metre

So the height of the taller building is 12 + 5 or 17 metres.