How do I find how tall a building is? How tall is a tower if it casts a shadow 65 ft. long at the same time that a building 160 ft. tall casts a shadow 130 ft. long?
I tried using the hypotenuse formula but didn't get the right answer. 
Help.
 A: As Arturo said, you need to use similar triangles. Here’s a picture to get you started:

The building and its shadow, together with the hypotenuse joining their ends, form a triangle similar to the one formed by the tower and its shadow. You know the lengths of both shadows and the height of the tower; now just use the fact that the large triangle is just a scaled up version of the smaller one: every side has been multiplied by the same amount.
A: If $\alpha$ is the angle that the Sun rays make with the Earth, then $\tan \alpha = \frac{h}{s} = \frac{h_1}{s_1}$, where $h,s$ are the height and shadow lengths of the first building and index one stands for the second building. Then, $h = \frac{s}{s_1} h_1 =\frac{65}{130}  160 = 80 ft$.
A: Toss a firecracker on to the street from the roof. It will fall at 30 feet per second, the speed of gravity. When it hits the ground the startled pedestrians below will likely swear in surprise. Their swear words will float back up to you at 1100 feet per second, the speed of sound. Therefore the length of time for you to hear swearing after you chuck the firecracker will be:
height/30 seconds + height/1100
= 
1100 x height / 33000 + 30 x height / 33000
=
1130 x height / 33000
therefore 
the building's height = 33000/1130 x the amount of seconds between when you dropped the cracker and when you heard people swearing at you.
Sometimes maths can be fun. But usually only when it involves things that explode.
