Question

A right triangle has perimater 7 and hypotenuse of length 3 , if A is the larger non right angle in the triangle , find Cos A

Answer 1

Answer:

$cosA=\dfrac{2-\dfrac{\sqrt{2} }{2} }{3}$

Step-by-step explanation:

Let's consider AB,BC and AC are sides of right angle triangle ABC in which hypotenuse is AC

Given,

hypotenuse of triangle, AC= 7

perimeter of triangle= 3

=> AB+BC+AC= 7

=>AB+BC= 4

=>BC=4-AB

according to Pythagoras theorem,

$height^{2} =hypotenuse^{2} -base^{2} \\ AB^{2} =AC^{2} -BC^{2} \\=> AB^{2} =3^{2} +(4-AB)^{2}$

$AB={2-\frac{\sqrt{2} }{2}$ (since, A is larger angle)

since,

$cosA=\dfrac{AB}{AC}\ (for\ angle\ A\ AB\ will\ be\ base)\\=\dfrac{2-\dfrac{\sqrt{2} }{2} }{3}$