A surveyor is 40m from the edge of a building. The angle of elevation from the surveyor to the top of the building is 55° . What is the height of the building?

Height of building is 57.12 m.

Step-by-step explanation:

Let us try to understand the given dimensions as per the attached diagram.

Please refer to attached image (Right angled )

with

Let O be the point where the Surveyor is standing.

B be the point of the base of building.

T be the point of top of building.

As per question statement,

Side OB = 40 m

To find: Side BT = ?

Using tangent trigonometric identity:

So, height of building is 57.12 m.

22 dimes and 9 nickels

step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4