The diagram shows an L-shaped dustpan $ABC$ leaning against a vertical wall. It is given that&nbsp

Question

The diagram shows an L-shaped dustpan $ABC$ leaning against a vertical wall. It is given that $AB = 20$ cm, $BC = 50$ cm, $\angle AOC = \angle ABC = 90{}^\circ$ and $\angle OCB = \theta{}^\circ$. Show that $AO + OC = (30 \cos \theta + 70 \sin \theta)$ cm. Find the value of $\theta$ for which $AO + OC = 65$ cm. State the maximum value of $(AO + OC)$ and the corresponding value of $\theta$.

Accepted Answer

(a) $AO+OC=(30\cos\theta+70\sin\theta)\text{ cm}$ (b) $\theta=35.4^\circ$ (c) $76.2\text{ cm}$ when $\theta=66.8^\circ$

Trigonometry - Trigonometric Modelling

Trigonometry - Trigonometric Modelling

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