Question 1042063
A ladder 2.5 m rests on a wall with its other end on the ground 1.5 m from the wall.
 A 0.2 vertical strut fits in between the ladder and the ground as shown.
a) What is the height of the top of the ladder which rests against the wall from the ground?
let a = the height of the top of the ladder from the ground
a right triangle is formed, the ladder is the hypotenuse
a^2 + + 1.5^2 = 2.5^2
a^2 + 2.25 = 6.25
a^2 = 6.25 - 2.25
a^2 = 4
a = 2 meters is the height of the top of the ladder
:
b) How far from the bottom end of the ladder would the 0.2 m vertical strut fit?
Find the angle (A) that the ladder makes with the ground using the cosine
where the hypotenuse is 2.5 and the side adjacent (ground) is 1.5
Cos(A) = {{{1.5/2.5}}}
Cos(A) = .6
A = 53.13 degrees
The strut forms a right angle with the ground
Use the tangent of 53.13 degrees where side opposite is .2 & side adjacent is the distance from the ladder (b) that we are looking for
Tan(53.13) = {{{.2/b}}}
1.33 = {{{.2/b}}}
1.33b = .2/1.33
b = .15 meters from the end of the ladder to the strut