Question

Select the correct answer. In right triangle ABC, b^2+c^2=34 and bc=15. What is the approximate length of side a? Note: Use the law of cosines.
(the triangle is a right triangle with an angle of 53)

Answer 1

Using the law of cosines, it is found that the approximate length of side a is 3.99 units.

What is the law of cosines?

The law of cosines states that we can find the side c of a triangle as follows:

$c^2 = a^2 + b^2 - 2ab\cos{C}$

in which:

• C is the angle opposite to side c.

• a and b are the lengths of the other sides.

In the context of this problem, we have that side a is opposite to the angle of 53º, hence:

$a^2 = b^2 + c^2 - 2bc\cos{53^\circ}$

We are given that:

• b² + c² = 34.

• bc = 15.

Then:

$a^2 = 34 - 30\cos{53^\circ}$

a² = 15.95

$a = \sqrt{15.95}$

a = 3.99.

More can be learned about the law of cosines at https://brainly.com/question/4372174

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