   Chapter 11.3, Problem 4E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

In Exercises 1 to 4, find tan α and tan β for each triangle. To determine

To find:

The values of tanα and tanβ for the triangle.

Explanation

Given:

The rectangle is shown below.

Definition used:

In a right triangle, the tangent ratio for an acute angle is the ratio oppositeadjacent.

Calculation:

From the figure we see that the rectangle is divided into two right triangles.

Consider the right triangle DCB.

Therefore we have BD=7,BC=3. Let DC=x.

In a right triangle, (hypotenuse)2=(opposite)2+(adjacent)2

(BD)2=(BC)2+(DC)2(7)2=(3)2+x27=3+x273=x24=x24=x2=x

Thus CD=2

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