Thread: Need help with this Angle of Depression question

Hi need some help with my homework, I'm 14 so it should be pretty easy to someone knowledgeable on the topic!

Two buildings, 15m and 27m high, are directly opposite each other across a river. The angle of depression of the top of the smaller building from the top of the taller building is 52 degrees.
How wide is the river?

Thanks in advance

Originally Posted by Cyb3rT3rr0r

Two buildings, 15m and 27m high, are directly opposite each other across a river. The angle of depression of the top of the smaller building from the top of the taller building is 52 degrees.
How wide is the river?

Draw a horizontal line indicating the distance between the buildings at the height of the shorter building (and thus also indicating the width of the river, assuming, contrary to "real life", that the buildings are directly on the river's banks). Label as "r".

Draw a vertical line at one end, indicating the (remaining) height of the taller building. Label as 27 - 15 = 8.

Draw a slanty line indicating the line of sight from the top of the shorter to the top of the larger building. Label the angle at the shorter building as 52 degrees.

Note that 8/r = tan(52 degrees)....