A surveyor is mapping a large marsh in a state park. He walks and measures a straight line south from a cliff for 0.75 mile to a large tree. He walks east, but he has to make a detour around the marsh. He gets around the marsh to a spot where he is perpendicular to the large tree and the trail he originally walked south on. He looks northwest and measures a 40° angle (ZA) northwest to the cliff from his line of sight to the large tree. He measures the distance back to the starting point at the cliff as 1.17 miles. What is the straight-line distance from the large tree east to ZA? What is the tangent of ZB , the angle at the cliff? Cif 075 mile 1.17 mile 40 Tree

A surveyor is mapping a large marsh in a state park. He walks and measures a straight line south from a cliff for 0.75 mile to a large tree. He walks east, but he has to make a detour around the marsh. He gets around the marsh to a spot where he is perpendicular to the large tree and the trail he originally walked south on. He looks northwest and measures a 40° angle (ZA) northwest to the cliff from his line of sight to the large tree. He measures the distance back to the starting point at the cliff as 1.17 miles. What is the straight-line distance from the large tree east to ZA? What is the tangent of ZB , the angle at the cliff? Cif 075 mile 1.17 mile 40 Tree

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Concept explainers

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.

Question

9. A surveyor is mapping a large marsh in a state park. He walks and measures a straight line south
from a cliff for 0.75 mile to a large tree. He walks east, but he has to make a detour around
the marsh. He gets around the marsh to a spot where he is perpendicular to the large tree and
the trail he originally walked south on. He looks northwest and measures a 40° angle (ZA)
northwest to the cliff from his line of sight to the large tree. He measures the distance back to
the starting point at the cliff as 1.17 miles. What is the straight-line distance from the large tree
east to ZA? What is the tangent of ZB , the angle at the cliff?
Clff
0.75 mile
1.17 mile
40
Tree

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