Concept explainers
To show: Two triangles ABC and
Answer to Problem 31E
The two triangles are provided below.
For triangle ABC , conditions are
For triangle
Explanation of Solution
Given information:
The
Formula used:
The sine rule for a triangle is
Calculation:
Consider the conditions,
Recall that the sine rule for a triangle is
From the above
Simplify it further as,
Now, there are two possible values for the angle B since the sine function is positive in first and second quadrant. So, value of angle B lies between
So, one value is
Therefore,
Now, similarly there will be two possible values for angle C also. Recall that sum of all angles of a triangle is
Now, for triangle ABC ,
Recall that the sine rule for a triangle is
Apply it to compute the length of side c ,
Now, for triangle,
Recall that the sine rule for a triangle is
Apply it to compute the length of side c ,
Therefore, for triangle ABC , conditions are
Therefore, for triangle
To show: The area of triangles ABC and
Explanation of Solution
Given information:
For triangle ABC , conditions are
For triangle
Formula used:
The area of a triangle is denoted by
Proof:
It is provided that for triangle ABC , conditions are
Recall that the area of a triangle is denoted by
Therefore, for side
For triangle
Recall that the area of a triangle is denoted by
Therefore, for side
Now,
And,
Hence, it is shown that the area of triangles ABC and
Chapter 6 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning