Explanation Consider the following figure, Let us put the name for the isosceles triangle ia ABC and altitude is A D ¯ We know that B D = D C = b a s e 2 Assume that B D = D C = x u n i t s General formula for cosine ratio and sin ratio is given below, cos θ = a d j a c e n t h y p o t e n u s e θ = cos − 1 ( a d j a c e n t h y p o t e n u s e ) and sin θ = o p p o s i t e h y p o t e n u s e θ = sin − 1 ( o p p o s i t e h y p o t e n u s e ) tan θ = o p p o s i t e a d j a c e n t For Δ A D B : From the above figure shows that the s is the value of hypotenuse since it is opposite to right angle. Then DC is the length of the leg opposite to θ . Therefore, cos θ = A D A B = A D s A D = ( cos θ ) s

Elementary Geometry For College Students, 7e

7th Edition

ISBN: 9781337614085

Author: Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher: Cengage,

See similar textbooks

Concept explainers

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.

Videos

Question

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Chapter 11.2, Problem 41E

To determine

To find:

To show that the area of the isosceles triangle is A=s2sinθcosθ by using the following figure,

Expert Solution & Answer

Chapter 11 Solutions

Elementary Geometry For College Students, 7e

Ch. 11.1 - In Exercises 1 to 6, find sin and sin for the...Ch. 11.1 - In Exercises 1 to 6, find sin and sin for the...Ch. 11.1 - In Exercises 1 to 6, find sin and sin for the...Ch. 11.1 - In Exercises 1 to 6, find sin and sin for the...Ch. 11.1 - In Exercises 1 to 6, find sin and sin for the...Ch. 11.1 - In Exercises 1 to 6, find sin and sin for the...Ch. 11.1 - In Exercises 7 to 14, use either Table 11.2 or a...Ch. 11.1 - In Exercises 7 to 14, use either Table 11.2 or a...Ch. 11.1 - Prob. 9E Ch. 11.1 - Prob. 10E

Knowledge Booster

$Geometry$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.

To show that the area of the isosceles triangle is A = s 2 sin θ cos θ by using the following figure,

Solution Summary: The author explains that the area of the isosceles triangle is A=s2mathrm

Concept explainers

Videos

To find:

To show that the area of the isosceles triangle is A=s2sinθcosθ by using the following figure,

Chapter 11 Solutions

To show that the area of the isosceles triangle is A = s 2 sin θ cos θ by using the following figure,

Solution Summary: The author explains that the area of the isosceles triangle is A=s2mathrm

Concept explainers

Videos

To find: To show that the area of the isosceles triangle is A=s2sinθcosθ by using the following figure,

Chapter 11 Solutions

To find:

To show that the area of the isosceles triangle is A=s2sinθcosθ by using the following figure,