a surveyor on level ground finds the angle of elevation of a 138-foot flagpole to be 47 degrees how far from the base of the pole is the surveyor?

I don't get any of this my teacher never shows us anything i have asked for help and he doesnt

ok, recipe for right triangle where hypotenuse is opposite right angle:

sin of angle = opposite side/hypotenuse
cos of angle = adjacent side / hypotenuse
tan of angle = opposite side/adjacent side

look at

http://www.regentsprep.org/Regents/math/algtrig/ATT1/trigsix.htm

you only really need sin, cos, tan for now.

thanks

To find the distance from the base of the pole to the surveyor, we can use trigonometry.

Let's denote the distance from the base of the pole to the surveyor as "x". We can form a right triangle where the height of the flagpole is the opposite side, the distance "x" is the adjacent side, and the angle of elevation (47 degrees) is the angle between the hypotenuse (line of sight from the surveyor to the top of the pole) and the adjacent side.

Using the tangent function, which relates the angle of elevation to the opposite and adjacent sides of a right triangle, we have:

tan(47 degrees) = opposite/adjacent
tan(47 degrees) = 138/x

Now, we can solve this equation for "x" by multiplying both sides by "x" and then dividing by tan(47 degrees):

x = 138 / tan(47 degrees)

Using a calculator, we can find:

x ≈ 138 / 1.0724
x ≈ 128.63 feet

Therefore, the surveyor is approximately 128.63 feet from the base of the pole.

Now Taylor, I told you to draw a picture.

what is adjacent side, what is opposite side, what is hypotenuse?

You are welcome, good luck !