The diagram shows four points $A$, $B$, $C$ and $O$ such that that $AB = 2$ m, \(BC =

Question

The diagram shows four points $A$, $B$, $C$ and $O$ such that that $AB = 2$ m, $BC = 10$ m, $\angle AOC = \angle ABC = 90{}^\circ$ and $\angle OCB = \theta{}^\circ$. Show that $OC = 2\sin \theta + 10\cos \theta$. Express $OC$ in the form $R\sin(\theta + \alpha)$. Find the maximum value of $OC$ and the corresponding value of $\theta$. Find the value of $\theta$ for which $OC = 8$ m.

Accepted Answer

(a) $OC=2\sin\theta+10\cos\theta$ (b) $OC=2\sqrt{26}\sin(\theta+78.7^\circ)$ (c) $OC_{\max}=2\sqrt{26}\text{ m}$ when $\theta=11.3^\circ$ (d) $\theta=49.6^\circ$

Trigonometry - Trigonometric Modelling

Trigonometry - Trigonometric Modelling

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