What is the length of BC? Round to the nearest tenth.

Mathematics

1 answer:

emmasim [6.3K]3 years ago

4 0

9514 1404 393

Answer:

Step-by-step explanation:

The relevant trig relation is ...

Sin = Opposite/Hypotenuse

sin(65°) = BC/BA

BC = BA·sin(65°) ≈ (16 cm)·0.9063 ≈ 14.501 cm

BC ≈ 14.5 cm

_____

<em>Additional comment</em>

As is often the case, a simple estimate is all that is needed to identify the correct answer choice.

You only need to know how the long side of a right triangle compares to the others. In an isosceles right triangle, both legs are √2/2 ≈ 0.71 times the hypotenuse. The long side of a right triangle will never be shorter than that. This means the long side must be greater than about 11.2, and cannot be greater than 16. There is only one answer choice in that range.

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