BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter C, Problem 46E

(a)

To determine

To show:

  A=12absinθ

Expert Solution

Explanation of Solution

Given information:

Length of two sides: a,b

Angle: θ

Formula Used:

The area of triangle is given by the following expression:

  A=12bh

Where,

Base: b

Height: h

Proof:

First sketch the triangle with two side length as a,b and includes an angle of θ . Then height h as perpendicular to the side b :

  Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter C, Problem 46E , additional homework tip  1

From figure:

  sinθ=hah=asinθ

So, the area of triangle is given by the following expression:

  A=12bhA=12b(asinθ)A=12absinθ

Hence, proved.

(b)

To determine

To calculate:

The area of ΔABC

Expert Solution

Answer to Problem 46E

The area of ΔABC is 14.34457cm2 .

Explanation of Solution

Given information:

  |AB|=10cm|BC|=3cmABC=107°

Formula Used:

The area of triangle is given by the following expression:

  A=12bh

Where,

Base: b

Height: h

Calculation:

  ΔABC is drawn as follow with the given information:

  Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter C, Problem 46E , additional homework tip  2

The area of triangle is given by the following expression:

  A=12bh

Put the given data:

  A=12bhA=12|AB||BC|ABCA=12(10×3×107)A=14.34457cm2

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