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# Find the area of triangle ABC

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Find the area of triangle ABC if AB = BC = 12 and angle ABC = 150 degrees.

Oct 30, 2020

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Find the area of triangle ABC if AB = BC = 12 and angle ABC = 150 degrees.

Since AB = BC triangle ABC is isoceles and angles BAC and BCA are equal

Since ABC = 150o and the sum of the interior angles of a triangle is 180o

then angles A and C total 30o and therefore each of them is 15o

Draw a perpendicular from the apex B down to a point on side AC - call the point P

BP

Using the sine function:    sin(15) = ———

12

BP = (12)(0.65029) = 7.80        this is the height of the triangle

AP

Using the cosine function:  cos(15) = ———

12

AP = (12)(0.96593) = 11.59       this is half the base of the triangle

So the whole base of the triangle is (2)(11.59) = 23.18              (We could have skipped this step.  Do you know why?)

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The formula for the area of a triangle is  — • base • height

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So, the area of this triangle is 0.5 • 23.18 • 7.80 = 90.40 units2

The answer in the back of the book might be slightly different, because of the rounding that happened here.

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Oct 30, 2020
edited by Guest  Oct 30, 2020