Answered: For the right triangle shown in the…

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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For the right triangle shown in the figure below, what are each of the following? (Let

y = 6.30 m

and

r = 6.50 m.)

A diagram of a right triangle with a hypotenuse labeled r, one leg labeled x and the other leg labeled y. The angle adjacent to x is labeled θ and the angle adjacent to y is labeled ϕ.

(a)

the length (in m) of the unknown side x

(b)

the tangent of θ

Apply the expressions for tangent of a base angle in a right triangle as a ratio of the sides of the triangle.

(c)

the sine of ϕ

Your incorrect answer may have resulted from roundoff error. Make sure you keep extra significant figures in intermediate steps of your calculation.

(d)

What if? Keeping the length found in (a) fixed, by what factor would the length of the 6.30 m side have to be changed for the angles θ and ϕ to be equal? (Let y' be the new length of the 6.30m side.)

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