   Chapter 5.5, Problem 18E 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 15 to 19, create drawings as needed. Given: ∆ X Y Z with X Y ¯ ≅ X Z ¯ ≅   Y Z ¯ Z W ¯ ⊥ X Y ¯ with W on X Y ¯ Y Z = 6 Find: Z W

To determine

To find:

ZW for the XYZ with XY¯XZYZ¯, ZW¯XY¯ with W on XY¯ and YZ=6.

Explanation

Approach:

For a right triangle, for which the measure of the interior angles 30°, 60°, and 90°; if ‘a’ is the length of measure of the shorter leg; opposite to the angle 30°, then the length of the other two sides is given by

Length of the longer leg (opposite to 60°) =a3

Length of the hypotenuse (opposite to 90°)=2a.

In general

Length of the longer leg =3× (Length of the shorter leg)

Length of the hypotenuse =2× (Length of the shorter leg)

Calculation:

Given,

For a XYZ with W on XY¯, XZYZ¯,

ZW¯XY¯

YZ=6.

Thus, we have

Since, if is given that XY¯XZ¯YZ¯, all the three sides of the XYZ is congruent and which forms XYZ as an equilateral triangle.

For am equilateral triangle all the three interior angles measures to be 60°.

Thus,

mX=mY=mZ=60°

In the above triangle the perpendicular line segment ZWXY divides the the XYZ

Into two right triangles as right the XWZ and right the ZWY.

Now, consider the right XWZ, in which we have right angle at W and mX=60°

With XZ=6

In the above we have XZ=6 and which is the hypotenuse of the triangle

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