In isosceles triangle XYZ, XY = XZ = 5.9 cm and YZ = 5.0 cm. What are the measures of the angles of the triangle to the nearest tenth of a degree?

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Answer 1 · 2017-12-04T12:29:08

Three angles are #64.9^0, 64.9^0 , 50.2^0#

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XY = XZ = 5.9 cm, YZ = 5 cm

As per the diagram above,
#(a/2) / b = cos /_ Y#

#a = 5, b = 5.9#

#:. cos /_ Y = (5/2) / 5.9 = 2.5 / 5.9 = 0.4237#

#/_ Y = cos ^-1 (0.4237) = 64.9^0#

As it’s an isosceles triangle, #/_ Y = /_ Z = 64.9^0#

#/_ X = 180 - /_ Y - /_ Z = 180 - 64.9 - 64.9 = 50.2^0#