The angle of elevation to the top of a fl agpole from a point 28 m from its base is 38°. How tall is the fl agpole, correct to two decimal p

You would use the tangent of the angle to find the height of the flagpole, h.

Tangent is opposite/adjacent, and in this problem the opposite side is the height of the pole (h) while the adjacent side is the length to the pole's base (28).

Therefore: 

tan(38) = opp/adj

tan(38) = h / 28

Multiply both sides by 28.

$${\mathtt{h}} = \underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}{\left({\mathtt{38}}^\circ\right)}{\mathtt{\,\times\,}}{\mathtt{28}} \Rightarrow {\mathtt{h}} = {\mathtt{21.875\: \!997\: \!542\: \!196}}$$

The flagpole is approximately 21.88 m tall.

We have an angle and its adjacent side...we need to find the opposite side....the tangent function relates these three things

tan(38) = x/28    where x is the flagpole height  ..so...

28tan(38) = 21.88 m