Anyone can show me the method?
1. In a triangle PQR, PQ=a, QR=a+d, RP=a+2d and , where a and d are positive constant, show that
2. A man observed the top of a tower from the points A, B and C along a straight, horizontal road, where AB=a and BC=b. The angle of elevation of the top of the tower from A is while the angle of elevation from B and C are both equal to . If is the angle of elevation of the top of the tower from the point E wich is the mid-point of BC, show that
i) is the largest angle of elevation,
Hello again cloud5
Suppose that is the foot and the top of the tower, and that . Then we have:For part (i):
is the shortest distance from the foot of the tower to .
Eliminate from (1) and (2) and the result follows.
Can you fill in the gaps?
are all horizontal lines, and therefore are perpendicular to . So from the right-angled triangles, we get:Thus , and is therefore isosceles, with the mid-point of . Hence:
The remaining working uses Pythagoras' Theorem on the right-angled triangles and .
is therefore the foot of the perpendicular from to
Therefore is the shortest distance from to , and so:
is therefore the largest angle of elevation of from the line