Question 58

For $$\theta$$ being an acute angle, $$4(2 \sin^2 \theta + 7 \cos^2 \theta) = 13$$. What is the value of $$\theta$$?

Solution

$$4(2 \sin^2 \theta + 7 \cos^2 \theta) = 13$$

$$4(2 \sin^2 \theta + 7 (1-\sin^2 \theta) = 13$$

$$4(7 - 5\sin^2 \theta) = 13$$

$$28 - 20\sin^2 \theta = 13$$

$$20\sin^2 \theta = 15$$

$$\sin^2 \theta = \frac{15}{20}$$

$$\sin^2 \theta = \frac{3}{4}$$

$$\sin \theta = \frac{\sqrt{3}}{2} $$

$$\theta= 60^\circ$$

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