Question

Solve the following problem.

Answer 1

Answer: C

Explanation:

Pythagorean's Theorem can only be used for right triangles. For the triangle above, the Law of Cosines must be used. The Law of Cosines can be used when you're given two sides and an angle. The general formula is below:

`x^2=a^2+b^2-2abcos(theta)`

For the triangle above:

a = 23

b = 20

∅ = 47°

Therefore:

`x=√(23^2+20^2-2*23*20*cos(47)) =√(529+400-920cos(47))=√(929-920cos(47)) =17.37`

Answer 2

(c) 17.37

Explanation:

You want the side opposite the 47° angle in a triangle with lengths 23 m and 20 m on either side of that angle.

Largest angle

The largest angle in any triangle will never be smaller than 60°. This means the angle 47° will not be the largest. The side opposite that angle cannot be the longest side, so cannot be greater than 23 m.

This eliminates all answer choices except 17.37 m, choice C.

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Additional comment

If you feel compelled to find the length x, you can use the law of cosines. It will tell you ...

x = √(23² +20² -2·23·20·cos(47°)) ≈ 17.37 . . . . meters

Often a multiple-choice question can be answered easily by eliminating the choices that make no sense.

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