Question 1174547
when it is leaning against the wall, the foot of the ladder is 2m from the base of the wall.
 The angle between the ladder and the ground is 75 degrees.


a) How high up the wall does the ladder reach, to the nearest centimetres?
Draw this out as a right triangle, it will be clear to you
Find the height (h) of the ladder using the tangent of the 75 degrees
(2 meters = 200 centimeters) height is side opposite,
tan(75) = {{{h/200}}}
200*tan(75) = h
h = 746 centimeters
:
b) How long is the ladder to the nearest centimetres?
Use the cosine, the ladder (L) is the hypotenuse
cos(75) = {{{200/L}}}
cos(75)*L = 200
.2588L = 200
L = {{{200/.2588}}} 
L = 773 centimeters
:
c) If the ladder slips down the wall so that it makes an angle of 55 degrees with the ground, does the end on the ground slip more than the end against the wall? Explain?
Ashamed to say I can't reason this out, will have to use sine * cos of 55 degrees
Find how far the ladder comes down
sin(55) = {{{h/773}}}
h = sin(55)*773
h = 633 cm
746 - 633 = 113 cm drop
:
Find the dist (d) base of the ladder moves out
cos(55) = {{{d/773}}}
d = cos(55)*773
d = 443 cm
443 - 200 = 243 cm further
:
Base of ladder slips about twice as far as the top of the ladder comes down.