You are standing nearby a tree with your eyes 2 metres above the ground. The line of sight to the top of the tree makes an angle of 60° with the horizontal. This angle reduces to 45° when you step back 4 metres further away from the tree, (a) How tall is the tree? (b) Suppose that you then step back another 2 metres further away from the tree. What angle does the line of sight to the top of the tree now make with the horizontal?
You are standing nearby a tree with your eyes 2 metres above the ground. The line of sight to the top of the tree makes an angle of 60° with the horizontal. This angle reduces to 45° when you step back 4 metres further away from the tree, (a) How tall is the tree? (b) Suppose that you then step back another 2 metres further away from the tree. What angle does the line of sight to the top of the tree now make with the horizontal?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Transcribed Image Text:1. You are standing nearby a tree with your eyes 2 metres above the ground. The line
of sight to the top of the tree makes an angle of 60° with the horizontal. This angle
reduces to 45° when you step back 4 metres further away from the tree,
(a) How tall is the tree?
(b) Suppose that you then step back another 2 metres further away from the tree. What
angle does the line of sight to the top of the tree now make with the horizontal?
2. Let A = (2,3), B = (5,7) and C = (3,5).
%3D
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(a) Determine the equations of the perpendicular bisectors l, m and n of the sides AB,
BC and CA of the triangle ABC respectively.
(b) Show that the lines l, m and n are concurrent at a point P, the circumcentre of
the triangle ABC. Determine the coordinates of P.
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