# trigonometry

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the height of a triangle is 10m longer than twice its base. its area is 176m^2. Find the lengths of its height and base.

• trigonometry -

base = x
height = 2x+10

(1/2)(x)(2x+10) = 176
2x^2 + 10x = 352
x^2 + 5x - 176 = 0
(x + 16)(x-11) = 0
x = -16 or x = 11 , but x > 0

so x = 11

base is 11, height is 32

check: (1/2)(11)(32) = 176

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