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The sides of an isosceles triangle are 14.0m, 14.0m, and 18.0m. Find the size of each angle of the triangle.

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The sides of an isosceles triangle are 14.0m, 14.0m, and 18.0m. Find the size of each angle of the triangle.

asked Aug 31, 2015 in PRECALCULUS by anonymous

1 Answer

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Draw the isosceles triangle:

In a isosceles triangle two sides and two angles are equal.

Find the angle x by using the sine rule:

14/sin x  = 18 / sin (180  2x)

Apply trigonometric angle formula: sin (180  x) = sin x

14/sin x  = 18 sin (2x)

Apply trigonometric double angle identities: sin (2x) = 2sin x cos x

14/sin x  = 18 2 sin x cos x

18 sin x  = 28  sin x cos x

9 sin x  = 14  sin x cos x

9 sin x  - 14  sin x cos x = 0

sin ( 9  - 14 cos ) = 0

sin = 0

π is not possible.

 - 14 cos = 0

cos x  = 9/14

 = 50 degree

180 - 2x = 80 degree

Therefore, the angles are 50,50, and 80.

answered Aug 31, 2015 by anonymous

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