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
Bundle: Precalculus, Loose-leaf Version, 10th + WebAssign Printed Access Card for Larson's Precalculus, 10th Edition, Single-Term
- Distance to a Ship A ship is anchored off a long straight shoreline that runs north and south. From two observation points 18 miles apart on shore, the bearings of the ship are N 31 E and S 53 E. What is the distance from the ship to each of the observation points?arrow_forwardRe-do the example under the assumption that the height of the tent 5 feet toward the center from the outside is 13 not 12 feet. The outside wall of the circus tent depicted in Figure 3.9 is 10 feet high. Five feet toward the center pole, the tent is 12 feet high. The center pole of the tent is 60 feet from the outside wall.arrow_forwardAir Navigation An airplane flying at 550 miles per hour has a bearing of 52. After flying for 1.5 hours, how far north and how far east will the plane have traveled from its point of departure?arrow_forward
- Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageHolt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningFunctions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningTrigonometry (MindTap Course List)TrigonometryISBN:9781305652224Author:Charles P. McKeague, Mark D. TurnerPublisher:Cengage Learning