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Chapter 8: Q. 34 (page 528)

Two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve each triangle that resultsb=4,c=5,B=95掳.

Short Answer

Expert verified

No triangle is possible from the given measurements.

Step by step solution

01

Step 1. Given information

b=4,c=5,B=95掳

For a triangle with sides a, b, c and opposite angles A, B, C, respectively, Law of sines is given as:

sinAa=sinBb=sinCc

02

Step 2. Calculation

ByLawofSines,ForC,鈬�sinBb=sinCc鈬�sinC=sinB脳cb=sin95掳脳54=0.9961脳1.25=1.245SincethereisnoangleCforwhichsinC>1,therecanbenotrianglewiththegivenmeasurements.

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Most popular questions from this chapter

Rework Problem 7 under the same conditions except that, at time t = 0, the object is at its resting position and moving down.

Find the area of the triangle. Round answer to two decimal places.

A=110掳,C=30掳,c=3

the displacement d (in meters) of an object at time t (in seconds) is givend=6+2cos(2蟺t)

(a) Describe the motion of the object.

(b) What is the maximum displacement from its resting position?

(c) What is the time required for one oscillation?

(d) What is the frequency?

Find the area of the triangle. Round answer to two decimal places.

A=40掳,B=20掳,a=2

Area of an ASA Triangle If two angles and the included side are given, the third angle is easy to find. The area K of the triangle with side a and angles A, B, and C is

K=a2sinBsinC2sinA

Area of a triangle Prove the two other forms of the above formula.

K=b2sinAsinC2sinBand K=c2sinAsinB2sinC
See all solutions

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