Chapter 5.5, Problem 18E

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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 30Â°, 60Â°, and 90Â°; if â€˜aâ€™ is the length of measure of the shorter leg; opposite to the angle 30Â°, then the length of the other two sides is given by

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

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

In general

Length of the longer leg =3Ã— (Length of the shorter leg)

Length of the hypotenuse =2Ã— (Length of the shorter leg)

Calculation:

Given,

For a âˆ†XYZ with W on XYÂ¯, â‰…XZâ‰…YZÂ¯,

ZWÂ¯âŠ¥XYÂ¯

YZ=6.

Thus, we have

Since, if is given that XYÂ¯â‰…XZÂ¯â‰…YZÂ¯, all the three sides of the âˆ†XYZ is congruent and which forms âˆ†XYZ as an equilateral triangle.

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

Thus,

mâˆ X=mâˆ Y=mâˆ Z=60Â°

In the above triangle the perpendicular line segment ZWâŠ¥XY divides the the âˆ†XYZ

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

Now, consider the right âˆ†XWZ, in which we have right angle at W and mâˆ X=60Â°

With XZ=6

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

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