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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

A 22-foot extension ladder leaning against a building makes a 70掳 angle with the ground. How far up the building does the ladder touch?

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

A=40掳,B=20掳,a=2

Designing an Awning An awning that covers a sliding glass door that is 88 inches tall forms an angle of 50掳 with the wall. The purpose of the awning is to prevent sunlight from entering the house when the angle of elevation of the Sun is more than 65掳. See the figure. Find the length L of the awning.

Find the distance from A to C across the gorge illustrated in the figure.

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

B=35掳,C=65掳,a=15
See all solutions

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