Area of triangle ABC

jejo1

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Feb 9, 2016
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If ABC is A triangle, AB = AC, BC = 16, COS(B =4/5, then find the area of ABC
 
If ABC is A triangle, AB = AC, BC = 16, COS(B =4/5, then find the area of ABC
I will guess that the capitalization in "A triangle" is a typo. If so, then you've been given an isosceles triangle. You know that you can split this down the middle to create two right triangles, each having a base whose length you can easily determine. (Check the drawing, if you're not sure about this.)

From the known length of the base of one of these right triangles, you can work backwards from the cosine to find the length of AB. Then apply the Pythagorean Theorem to find the value for the height. Then plug the value for the base of the original triangle, along with the height that you just found, into the formula for the area of a triangle.

If you get stuck, please reply with a clear listing of your efforts, showing what you did for each of the steps described above. Thank you! ;)
 
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