a.)at what rate is the lenght of her shadow increasing?
b.)at what speed is the tip of her shadow moving?
Step 1
Please have a look at the picture below to understand what's going on:
For the sake of clarity,
s = length of the shadow = AD
and x = distance of the lady from the wall = BD
Step 2
Triangle ADE is similar to triangle ABC (AAA criterion of similarity)
Hence,
Hence,
Hence,
Or,
Step 3
Part (a)
Differentiate both sides w.r.t time t to get:
Hence, the rate at which length of her shadow is increasing =
Step 4
Part (b)
the rate at which the tip of her shadow is moving = rate t which she is moving + rate at which the length of the shadow is increasing =
Step 5
Final answers:
Part (a)
Part (b)
Find the point on the line
Determine whether the polygons to the right are similar. If so, write a similarity statement and give the scale factor. If not, explain.
A.Tes,
B.No, because lengths of corresponding sides are not proportional.
C.Yes,
D.No, because corresponding angles are not congruent.
E.Yes,
F.Yes,
To prove:The two triangles are similar using postulate or theorem.
Given information:
The system triangles: