Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 7 - Section 7.1 - The Law of Sines - 7.1 Problem Set: 30

Answer

The person is $1377$ ft from the building when she makes her second observation.

Work Step by Step

Find the angles of the larger triangle that includes both triangles $\angle A = 90˚$ $\angle B = 28˚$ $\angle C = 180 - (90+28)$ $= 62˚$ 2. Find the angles inside the smaller triangle on the left side $\angle A = 180 - 38$ $= 142˚$ $\angle B = 28˚$ $\angle C = 180 - (142 + 28$ $= 10˚$ 3. Find the angles inside the large triangle on the right side $\angle A = 90˚$ $\angle B = 38˚$ $\angle C = 62 - 10 = 52˚$ 4. Use the sine law to solve for the missing length of the small triangle on the left $\frac{x}{sin(28)} = \frac{440}{sin(10)}$ $x = \frac{440sin(28)}{sin(10)}$ by GDC / calculator $x = 1189.574.... $ft 5. Use the answer in #4 to solve for the missing angle in the large triangle $\frac{y}{sin(52)} = \frac{1189.574...}{sin(90)}$ $y = \frac{1189..sin(52)}{1}$ $y = 937.39...$ ft 6. Add up the previous length with the known length of $440$ ft $= 937.39... + 440$ $=1377$ ft Therefore the person is $1377$ ft from the building when she makes her second observation.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.