Question

if a equal 43 B = -1, Y and c = 3, 4 are the vertices of the right angle triangle ABC A = 90 degree then find the value of Y​

Answer 1

The value of y=-2

Step-by-step explanation:

In triangle ABC

Angle A=90 degree

A(4,3),B(-1,y) and C(3,4)

Distance formula:$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Using the formula

$AB^2=(-1-4)^2+(y-3)^2=25+y^2-6y+9=y^2-6y+34$

$BC^2=(3+1)^2+(4-y)^2=16+16+y^2-8y=y^2-8y+32$

$AC^2=(3-4)^2+(4-3)^2=1+1=2$

Using identity:

$(a-b)^2=a^2+b^2-2ab$

Pythagoras theorem:$(hypotenuse)^2=(Base)^2+(Perpendicular\;side)^2$

Using Pythagoras theorem

$BC^2=AC^2+AB^2$

Substitute the values

$y^2-8y+32=2+y^2-6y+34$

$y^2-8y+32-y^2+6y=36-32$

$-2y=4$

$y=\frac{4}{-2}=-2$

Hence, the value of y=-2

#Learn more:

https://brainly.in/question/15779697