25. The sides of a parallelogram have lergtho of 18 anA 26 t and one angle f 29. Find the long th of the longer diagonal.

Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
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25. The sides of a
parallelogram have lergtho of 18 anA 26
t and one angle f 29. Find the long th of the longer diagonal.
Transcribed Image Text:25. The sides of a parallelogram have lergtho of 18 anA 26 t and one angle f 29. Find the long th of the longer diagonal.
Expert Solution
Step 1

Consider a paralog ram ABCD. Let AB=26 cm. and AD=18 cm. and angle A is 39 degrees.

Trigonometry homework question answer, step 1, image 1

For a polarogram, opposite sides are parallels and equal in length. The diagonals drawn by cutting the two opposite acute angles will be the largest diagonal for a polarogram.

Trigonometry homework question answer, step 1, image 2

Thus, in figure the diagonal AC is greater than the diagonal BD, since diagonal AC is drawn by connecting the acute angles.

Step 2

Extend the side AD and mark point E in such a way that EC is perpendicular to AE.

Consider the right angle triangle CBE.

The length of the side BE is,

Trigonometry homework question answer, step 2, image 1

The angle EBC and angle B will be equal because they are the corresponding angles formed by cutting a pair of parallel lines.

Trigonometry homework question answer, step 2, image 2

The expression to calculate the length of side CE is,

Trigonometry homework question answer, step 2, image 3

Substitute values in the above expression.

Trigonometry homework question answer, step 2, image 4

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