Question

If A(-2,2),B(5,2) and C(k,8)are the vertices of a right angle triangle ABC with angle B=90°,then find the value of k

Answer 1

Answer:

5

Step-by-step explanation:

since the triangle is right angled at B, k=5

Answer 2

The value of k is 5.

Explanation:

Given : A(-2,2),B(5,2) and C(k,8)are the vertices of a right angle triangle ABC with angle B=90°.

Using distance formula : $D=\sqrt{(c-a)^2+(d-b)^2}$ , where D is distance between (a,b) and (c,d).

$AB=\sqrt{(5-(-2))^2+(2-2)^2} =\sqrt{(7)^2+0^2}=7\ units$

$AC=\sqrt{(k-(-2))^2+(8-2)^2} =\sqrt{(k+2)^2+6^2}=\sqrt{(k+2)^2+36}\ units$

$BC=\sqrt{((k-5)^2+(8-2)^2} =\sqrt{(k-5)^2+6^2}=\sqrt{(k-5)^2+36}\ units$

Using Pythagoras Theorem ,

$AC^2= AB^2+BC^2$   [AC is opposite to angle B is the Hypotenuse of triangle]

$(\sqrt{(k+2)^2+36})^2= 7^2+(\sqrt{(k-5)^2+36})^2$

$(k+2)^2+36=49+(k-5)^2+36$

$k^2+2^2+2(k)(2)+36=49+k^2+5^2-2(k)(5)+36$

$k^2+4+4k+36=49+k^2+25-10k+36$

$4k+40=110-10k$

$4k+10k=110-40$

$14k=70$

$k=5$   [Divide both sides by 14]

Hence , the value of k is 5.

#Learn more :

In an right triangle the sq of hypotenuse is 50 cm if legs of right triangle are equal find the legs of right triangle​

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