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solmaris [256]
3 years ago
11

A, B & C form the vertices of a triangle.

Mathematics
1 answer:
Savatey [412]3 years ago
4 0

Answer:

BC = 17.2.

Step-by-step explanation:

Since CAB = 90º, this is a right triangle.

The triangle format is given below:

C

A           B

We have that AB = 8.6, and angle B measures 60º.

Length of BC:

BC is the hypotenyse.

Side AB is adjacent to angle B = 60º.

In a right triangle, angle \alpha, it's adjacent side with length s and the hypotenuse h are related by the cosine of the angle, that is:

\cos{\alpha} = \frac{s}{h}

In this question, we have an angle of 60º, with has cosine 0.5. We also have that side AB = s = 8.6, and the hypotenuse h is side BC. So

\cos{\alpha} = \frac{s}{h}

0.5 = \frac{8.6}{h}

0.5h = 8.6

h = \frac{8.6}{0.5}

h = 17.2

BC = 17.2.

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