3. a utility pole is 38 ft tall. the pole creates a 53 ft shadow. what is the angle of elevation of the sun? round your answer to the nearest degree. show your work

The angle of elevation of the sun is .

Step-by-step explanation:

Let be the angle of elevation of the sun as shown in the diagram.

Then the side length which is feet is opposite to and the side length which is feet is adjacent to .

Therefore we use the trigonometric ratio that involves the opposite and adjacent sides, which is the tangent ratio.

We solve for to get,

To the nearest degree, the angle of elevation is

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

answer: no

step-by-step explanation: because the big angle will spread away the 2 side that it is on and make the opposite side even longer.