Trigonometry quadratic equation

henna_naz · #1 May 15, 2008, 10:09 AM

Can you please help me on this, i have just seen that somebody else has asked this question previously but i dont understand how you manage to get two lengths.

Trigonometric Question:-
In triangle ABC, the angle A is 42 degrees, the side AB is 16cm and the side BC is 14cm. Find the two possible values of the side AC. How do you get two lengths?

ebaines · May 16, 2008, 01:31 PM

One way to solve this is to use the law of cosines, which states:

$<br /> A^2 + B^2 -2AB cos(C) = C^2<br />$

Here you can substitute 16 for length A, 14 for length C and 42 degrees for angle C, and solve for length B. Because it's a quadratic equation, you'll get two values for length B. See the attached figure and you'll see how that works - the third side of the triangle can be either BC or BC'.



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