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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 7: Q. 99 (page 497)

Area of an Isosceles Triangle Show that the area $A$ of an isosceles triangle whose equal sides are of length $s$ and $胃$ is the angle between them is
$A = \frac{1}{2} s^{2} \sin 胃$
[Hint: See the illustration. The height $h$ bisects the angle $胃$ and is the perpendicular bisector of the base.]

Short Answer

Expert verified

The area is $A = \frac{1}{2} s^{2} \sin 胃$

Step by step solution

01

Given information

Given length of isosceles triangle as $s$ and $胃$ is angle between them

02

Use the formula for area of a triangle and calculate

The area of a triangle is $A = \frac{1}{2} b h$ so we can write as follows;

$h = s \cos (\frac{胃}{2})$

Base will be $\frac{b}{2} = (\frac{胃}{2}) b = 2 s \sin (\frac{胃}{2})$

03

Substitute into formula for area of a triangle

Substituting, we get

$A = \frac{1}{2} b h A = \frac{1}{2} 路 2 s \sin (\frac{胃}{2}) 路 S \cos (\frac{胃}{2}) A = \frac{1}{2} 路 2 s \sin (\frac{胃}{2}) 路 S \cos (\frac{胃}{2}) A = s^{2} \sin (\frac{胃}{2}) \cos (\frac{胃}{2}) A = s^{2} 路 \frac{1}{2} \sin 胃 A = \frac{1}{2} s^{2} \sin 胃$

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Most popular questions from this chapter

Establish each identity.

$\frac{{(s e c v - \tan v)}^{2} + 1}{c s c v (s e c v - \tan v)} = 2 \tan v$

Establish each identity.

$\tan 胃 + c o t 胃 = s e c 胃 c s c 胃$

Show that $\sin^{- 1} (v) + \cos^{- 1} (v) = \frac{蟺}{2}$

Suppose that f and g are two functions with the same domain. If $f (x) = g (x)$ for every x in the domain, the equation is called a(n) ____. Otherwise, it is called a(n) _____ equation.

if $\sin 伪 = - \frac{4}{5}$ , $蟺 < 伪 < \frac{3 蟺}{2}$ , then $\cos 伪 =$ _____

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