If \angle ABD=\theta, then what is \sin\theta equal to?
Consider the following for the next three (03) items that follow:<br>In the triangle ABC, AB=6 cm, BC=8 cm and AC=10 cm. The perpendicular dropped from B meets the side AC at D. A circle of radius BD (with centre B) cuts AB and BC at P and Q respectively as shown in the figure.
- A. 0.4
- B. 0.5
- C. 0.6 ✓
- D. 0.8
Correct Answer: C. 0.6
Explanation
In \triangle ABD, since BD \perp AC, \angle A = 90^{\circ} - \theta. In the large right \triangle ABC, \angle C = 90^{\circ} - \angle A = \theta. Therefore, \sin\theta = \sin C = \frac{AB}{AC} = \frac{6}{10} = 0.6.
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