   Chapter 5.5, Problem 13E 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 5 to 22, find the missing lengths. Give your answers in both simplest radical form and as approximations correct two decimal places. Given: Rectangle H J K L with diagonals H K ¯ and J L ¯ m ∠ H K L = 30 ° and L K = 6 3 Find: H L , H K , and M K To determine

To find:

HL, HK, MK of the rectangle HJKL with daiagonals HK¯ and JL¯, mHKL=30° and LK=63.

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,

The rectangle HJKL

mHKL=30°

LK=63.

Thus,

Now, consider the triangle HKL of the rectangle HJKL which is by the division of the rectangle by the diagonal HK.

The right triangle HKL with m30° and LK=63.

Since, one of the acute angle mK of the right triangle is 30°, then the other acute angle mH should be 60°.

Thus, the HKL is of the type 30°-60°-90° triangle.

30°-60°-90° theorem.

In a right triangle whose angle measure 30°, 60°, and 90°, 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

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