Can ww specialements in similar angles to solve alworld problems. Real World Example 2 Wie Simariages to solve probleme
ESTIMATING DISTANCES Wiliana holda her arm straight out in front of her with the
hur thumb with a car she is sighing whes eyes without moving her
heat or her arm. The car appears to jumpa bar widths, 1 Liliana's arm is able
to time longer than the distance between her well, and the car is about so feel
wide estimate the distance from Liliana's thumb to the car.
Understand Make a diagram of the situation labeling the given distances and other
distance you need to find as the label the vertices of the triangles
formed
Image of the
Eye Cound
Thumb
25
55
Eyes
Image of Car with
Le Eye Closed
Note: Not down to scale
We assume that it Liliana's thumb is straight out in front of her then
PC is an altitude of AABC, Likewise, QC is the corresponding altitude.
We assume that AB | DF,
Plan Since AB || DEZBAC ZOTC and CBA a CDF by the Alternate
Interior Angles Theorem. Therefore AABC - AFDC by AA Similarity
Write a proportion and solve for x.
Solveig
Theorem 0.B
Substitution
Simplity
10.22 x 1
Cross Products Property
220
Simplity
So the estimated distance to the car is 220 feet.
Check The ratio of Liliana's arm length to the width between her eyes is 10 to 1.
The ratio of the distance to the car to the distance the image of the car
jumped is 22 to 220 or 10 to 1. V
Gulded Practice
2. Suppose Liliana stands at the back of her classroom and sights a clock on the wall
at the front of the room. If the clock is 30 centimeters wide and appears to move
3 clock widths when she switches eyes, estimate the distance from Liliana's thumb
to the clock
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