Chapter 5.5, Problem 4E

### 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

# For the 30 ° - 60 ° - 90 ° triangle shown, suppose that X Y = 2 a . Find: a) X Z b) Y Z

To determine

a) To find:

XZ, for the 30°-60°-90° triangle shown, suppose that XY=2a.

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,

A 30Â°-60Â°-90Â° triangle XYZ with XY=2a.

30Â°-60Â°-90Â° theorem.

In a right triangle whose angle measure 30Â°, 60Â°, and 90Â°, the hypotenuse has a length equal to twice the length of the shorter leg, and the longer leg is the product of 3 and the length of the shorter leg

To determine

b) To find:

YZ, for the 30°-60°-90° triangle shown, suppose that XY=2a.

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