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,
ii)
Hello again cloud5... and here's the outline for number 2.
Suppose that is the foot and the top of the tower, and that . Then we have:For part (i):
is isosceles(ii)
is the shortest distance from the foot of the tower to .
So?
(1)
Eliminate from (1) and (2) and the result follows.
(2)
Can you fill in the gaps?
Grandad
Hello cloud5Look at the attached diagram.
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
Grandad