Distance. In the figure, a beam of light is directed at the blue mirror, reflected to the red mirror, and then reflected back to the blue mirror. Find PT, the distance that the light travels from the red mirror back to the blue mirror.
To find:
The distance PT traveled by the light from the red mirror back to the blue mirror if the beam of light is directed at blue mirror, reflected to the red mirror, and then reflected back to the blue mirror.
Answer to Problem 1PS
Solution:
The distance is
Explanation of Solution
Formula:
Law of Cosines:
The formula for Law of Cosines is given by
Law of Sines:
The formula for Law of Sines is given by
Calculation:
Consider a beam of light which is directed at the blue mirror, reflected to the red mirror and then reflected back to the blue mirror as shown in the figure.
The required distance is PT. The distance PT can be calculated only if the length of the either of the sides of the triangle OPQ. So, use Cosine Law to calculate the side PQ. So,
Take square root. So,
Use the same triangle OPQ and use Sine Law to calculate the angle
Take arcsine on both the sides of the equation.
Denote the angle TPQ by
Use the fact that some of the angles in a straight line is
It is obtained that
Use this value in
Denote the angle PTQ by
Now, denote the angle PTO by
Use the Law of Sines for the triangle OPT to calculate PT. So,
Thus, the distance traveled by the light is
Final Statement:
The light travels a distance of
Want to see more full solutions like this?
Chapter 6 Solutions
Precalculus (MindTap Course List)
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageFunctions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningElementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillHolt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL