You have a right triangle formed by the ground, the pole and the line of sight from the point 40 m away on the ground and the top of the pole. It is assumed that the ground is flat and level.
Draw your triangle and label what you know. From the trig relationships that you have memorized (What? You haven't memorized them yet? Do it. Get over it.), you can see that the tangent relationship is what will help most, since it includes one angle and both sides.
Tangent is opposite over adjacent. Refer to your drawing to see which leg is opposite the angle and which is adjacent,
If you draw it you will see a right triangle with the base being 40 m and the angle adjacent to the base being 28º. You are looking for the height, which is the opposite of that angle so you can use tangent rules for right triangles:
Comments
Always draw a picture for this type of problem.
You have a right triangle formed by the ground, the pole and the line of sight from the point 40 m away on the ground and the top of the pole. It is assumed that the ground is flat and level.
Draw your triangle and label what you know. From the trig relationships that you have memorized (What? You haven't memorized them yet? Do it. Get over it.), you can see that the tangent relationship is what will help most, since it includes one angle and both sides.
Tangent is opposite over adjacent. Refer to your drawing to see which leg is opposite the angle and which is adjacent,
tan(28) = X/40
X = 40*tan(28)
Done
Always draw a picture of the problem
tan 28° = x / 40
x = 40 tan 28°
x = 21.3 m________height of flagpole
If you draw it you will see a right triangle with the base being 40 m and the angle adjacent to the base being 28º. You are looking for the height, which is the opposite of that angle so you can use tangent rules for right triangles:
tan() = opp/adj
So we have:
tan(28) = x/40
solve for x:
x = 40 tan(28)
x = 21.268 m (rounded to 3DP)
"From a point 40 m away from the base of a flagpole"
That's the adjacent of the angle
"the angle of elevation of the top is 28º."
That's the angle.
"Determine the height of the flagpole."
That's the opposite of the angle.
What trig function relates opposite and adjacent? The tangent.
tan(theta) = opposite/adjacent
Plug in the two numbers you know and solve for the other one.