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Chapter 8: Q. 49 (page 542)

Show that a formula for the altitude h from a vertex to the opposite side aof a triangle is

h=asinBsinCsinA

Short Answer

Expert verified

We showed that the altitude formula is h=asinBsinCsinA

Step by step solution

01

Given information

We are given that altitudehand side asa

02

Write the formula for area of triangle

We have,

K=12absinCK=12ah

Now we compare both formulas we get,

h=bsinC

03

We multiply numerator and denominator by sinB

We get,

h=sinBsinBbsinC

by law of sines we have,

asinA=bsinB=csinC

asinA=bsinB

Substituting this in the above equation we get,

h=sinBasinAsinCh=asinBsinCsinA

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Most popular questions from this chapter

The motion of an object obeys the equation d=4cos(6t)Such motion is described as ______ ______ . The number 4

is called the _____.

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

A=10°,a=3,b=10

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

Solve each triangle.

a=3,b=3,c=2

The displacement d (in meters) of an object at time t (in seconds) is given as d=5sin(3t)

(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?
See all solutions

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