Explanation:
there are just some big words trying to confuse you.
it just means that there is a right-angled triangle :
there is the point on the ground, where the surveyor is standing.
then there is the elevated point up there, where the surveyor was measuring the angle to.
and then there is the point on the ground directly under this elevated point. at this point in the ground we have the right angle (90°).
this height of the elevated point above this ground point is what we are looking for, and it is one leg of the right-angled triangle.
the ground distance from the surveyor to the ground point under the elevated point is 5 miles and the second leg.
the direct line of sight from the surveyor to the elevated point is inclined up by 20°, and is the Hypotenuse (baseline opposite of the 90° angle) of the triangle.
remembering that the sum of all angles in a triangle is always 180°, we also know the angle at the elevated point :
180 - 90 - 20 = 70°
now we are using the law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
where the sides are always opposite to their associated angles.
so, we have in our triangle
height/sin(20) = 5/sin(70)
height = 5×sin(20)/sin(70) = 1.819851171... miles
so, the elevated point is 1.819851171... miles above the elevation of the surveyor.