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Chapter 8: Q. 21 (page 541)

Find the area of a triangle whose sides are a=2,b=2,c=2.

Short Answer

Expert verified

Required area of the triangle is1.73squareunits

Step by step solution

01

Step 1. Given information

The area of a triangle with sides a, b, and c is determined by the Heron's formula which is given as:

Area=ss-as-bs-cwhere,s=a+b+c2

02

Step 2. Calculation

Given,a=2,b=2,c=2Then,s=a+b+c2=2+2+22=62=3Now,Heron'sformulagivesareaasArea=ss-as-bs-c=33-23-23-2=3×1×1×1=3=1.73squareunits

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Most popular questions from this chapter

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

an object attached to a coiled spring is pulled down a distance a from its rest position and then released. Assuming that the motion is simple harmonic with period T, write an equation that relates the displacement d of the object from its rest position after t seconds. Also assume that the positive direction of the motion is up:

a=5.T=2seconds

In the given problem solve the triangle using either the law of sines or law of cosines-

a=14,b=7,A=85°

the displacement d (in meters) of an object at time t (in seconds) is givend=4+3sin(πt)

(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?

An object of mass m (in grams) attached to a coiled spring with damping factor b (in grams per second) is pulled down a distance a (in centimeters) from its rest position and then released. Assume that the positive direction of the motion is up and the period is T (in seconds) under simple harmonic motion.

(a) Develop a model that relates the distance d of the object from its rest position after t seconds.

(b) Graph the equation found in part (a) for 5 oscillations using a graphing utility.

Given values:m=20,a=15,b=0.75,T=6
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