## Trigonometry (11th Edition) Clone

Published by Pearson

# Chapter 2 - Acute Angles and Right Triangles - Section 2.1 Trigonometric Functions of Acute Angles - 2.1 Exercises - Page 54: 53

#### Answer

$\sec$ 30$^{\circ}$ = $\frac{2\sqrt3}{3}$

#### Work Step by Step

$\sec$ 30$^{\circ}$ We must find side $x$ of the 30$^{\circ}$ - 60$^{\circ}$ Right Triangle. Pythagorean Theorem: $c$$^{2} = a$$^{2}$ + $b$$^{2} 2^{2} = 1^{2} + x$$^{2}$ 4 = 1 + $x$$^{2}$ x$^{2}$ = 3 x = $\sqrt 3$ Now consider the triangle from the perspective of the 30$^{\circ}$ angle. Hypotenuse = 2 Opposite = 1 Adjacent = $\sqrt 3$ $\sec$ 30$^{\circ}$ = $\frac{Hypotenuse}{Adjacent}$ = $\frac{2}{\sqrt 3}$ = $\frac{2\sqrt3}{3}$ Therefore: $\sec$ 30$^{\circ}$ = $\frac{2\sqrt3}{3}$

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