## Trigonometry 7th Edition

Published by Cengage Learning

# Chapter 2 - Section 2.2 - Calculators and Trigonometric Functions of an Acute Angle - 2.2 Problem Set: 68

#### Answer

$\theta$ = $84^{\circ}30'$

#### Work Step by Step

Given, $\sin\theta$ = $0.9954$ Therefore- $\theta$ = $\sin^{-1} 0.9954$ Given $\theta$ is between $0^{\circ}$ and $90^{\circ}$, i.e. lies in QI Using calculator in degree mode-(0.9954 → $\sin^{-1}$) $\theta$ = $(84.502273052) ^{\circ}$ $\theta$ = $84^{\circ} + (0.502273052)^{\circ}$ $\theta$ = $84^{\circ} +( 0.502273052\times60)'$ (Recall $1^{\circ}$ = $60'$) $\theta$ = $84^{\circ} +30'$ (Rounding to the nearest minute) $\theta$ = $84^{\circ}30'$

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