Log In Start studying!

Select your language

Suggested languages for you:

Americas

English (US)

Europe

Q3.

Expert-verified

Geometry

Found in: Page 583

Book edition Student Edition

Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

Pages 227 pages

ISBN 9780395977279

Answers without the blur.

Just sign up for free and you're in.

Register for Free I’ll do it later

Short Answer

A person with eyes at A, 150 cm above the floor, faces a mirror 1 m away. The mirror extends 30 cm above eye level. How high can the person see on a wall 2 m behind point A?

The person can see 2.7 m high on a wall 2 meter behind him.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information.

The eye of the person is at point A, 150 cm above the floor.

The wall is 2 m behind the person.

The mirror extends 30 cm above eye level.

The person faces mirror at a distance of 1 m.

Step 2. Calculation.

Angle made by the ray connecting mirror and eye with horizontal

$\begin{array}{l} \tan θ = \frac{\frac{30}{100}}{1} \\ = 16.7 ° \end{array}$

Thus angle made by the ray connecting mirror and eye with the normal of the mirror is also $16.7 °$ (alternate interior angles between parallel lines are equal).

According to the law reflection the reflected ray will also make same angle with the normal of the mirror.

Therefore, angle of reflection is $16.7 °$ .

Consider the height of wall above mirror level which the person can see be x m.

$\begin{matrix} \tan 16.7 ° = \frac{x}{3} \\ 0.3 = \frac{x}{3} \\ x = .9 [multiply each side by 3] \end{matrix}$

The height of wall from floor level which the person can see is

$\frac{150}{100} + \frac{30}{100} + 0.9 = 2.7$

Step 3. Conclusion.

Therefore the person can see 2.7 m high on a wall 2 meter behind him.

Most popular questions for Math Textbooks

Write the coordinates of the image of each point by reflection in,

The $x - a x i s$
The $y - a x i s$
The line $y = x$ (Hint: Refer to the Example on page 578)

Point O.

For each transformation given:

Plot the three points $A (0, 4)$ , $B (4, 6)$ , and $C (2, 0)$ and their images $A'$ , $B'$ , and $C'$ under the transformation.
State whether the transformation appears to be an isometry.
Find the pre image of $(12, 6)$ .

$H : (x, y) \to (- x, - y)$

Copy each figure on graph paper. Then draw the image by reflection in line k.

In Exercise 18-20, refer to the diagrams om page 578. Given the reflection $R_{m} : \vec{P Q} \to \vec{P' Q'}$ , write the key steps of a proof that $P Q = P' Q'$ for each case.

Case 4.

Draw a triangle and a line m such that $R_{m}$ maps the triangle to itself. What kind of triangle did you use?

Want to see more solutions like these?

Sign up for free to discover our expert answers

Get Started - It’s free

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.

Sign up for free