the-opposite-side-of-a-triangle-is-x-y-and-the-hypotenuse-is-3x-y-Given-that-that-A-is-an-acute-angle-find-the-value-of-Cos-A-

Question Number 36239 by Rio Mike last updated on 30/May/18

the opposite side of a triangle is

x + y, and the hypotenuse is 3 x + y

Given that that A is an acute angle

find the value of Cos A

Commented by Rasheed.Sindhi last updated on 30/May/18

Opposite side to ∠ A = x + y

Hypotenuse = 3 x + y

Adjacent side to ∠ A = \sqrt{{(3 x + y)}^{2} - {(x + y)}^{2}}

= \sqrt{{9 x}^{2} + 6 xy + y^{2} - x^{2} - 2 xy - y^{2}}

= \sqrt{{8 x}^{2} + 4 xy}

= 2 \sqrt{x (2 x + y)}

\cos A = \frac{2 \sqrt{x (2 x + y)}}{3 x + y}