Mathematics

Mathematics

Problem

In △ABC\triangle ABC, ∠B=90∘\angle B = 90^{\circ} with AB=6 cmAB = 6\,\text{cm}, BC=8 cmBC = 8\,\text{cm} and AC=10 cmAC = 10\,\text{cm}. For the acute angle θ\theta at vertex AA, which of the following equals cos⁡θ\cos\theta? a) 106\dfrac{10}{6} b) 610\dfrac{6}{10} c) 86\dfrac{8}{6} d) 810\dfrac{8}{10}
Intuitive explanation

This is about identifying which side ratio gives you the cosine of an angle in a right triangle. Remember that cos⁡θ\cos\theta always equals the ratio of the adjacent side to the hypotenuse — the key is figuring out which side is which from angle AA's perspective. Since ∠B\angle B is the right angle, ACAC must be the hypotenuse, and you need to identify which of the two remaining sides touches angle AA.

Intuitive explanation

This is about identifying which side ratio gives you the cosine of an angle in a right triangle. Remember that cos⁡θ\cos\theta always equals the ratio of the adjacent side to the hypotenuse — the key is figuring out which side is which from angle AA's perspective. Since ∠B\angle B is the right angle, ACAC must be the hypotenuse, and you need to identify which of the two remaining sides touches angle AA.

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