Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 1 - Section 1.1 - Angles, Degrees, and Special Triangles - 1.1 Problem Set: 23

Answer

α and β are complementary angles.

Work Step by Step

In given figure 22, producing the line DC along vertical post to meet the horizontal at "B"- a right triangle ABC, right angled at B is formed as vertical posts are perpendicular to the horizontal- In right triangle ABC- $ \angle A$ = α (Given) $ \angle C$ = β ( Vertically opposite angles are same at intersection of two lines ) Therefore- α + β = $90^{\circ}$ (Sum of acute angles of a right triangle is always $90^{\circ}$ Hence α and β are complementary angles.
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