Question

If LN=8 and MN=17, what is KN?

Write your answer as a whole number or as a decimal rounded to the nearest hundredth.
KN =

Answer 1

KN=3.765

As shown in the figure,

KM-KN+MN

Substitute MN=17 into KM-KN+MN:

KM-KN+17

`\angle LKN =\angle LKM` (same angles of the two triangles).

cos A=
`(leg \ adjacent \ to\angle A )/(hypotenuse \ KN)`

`cos (\angle LKN)= (KN)/(KL)`

`cos (\angle LKM)= (KL)/(KM)`

`(KN)/(KL)=(KL)/(KN+17)`

`KL^2=KN^2+17`

`KN=√(17+KN)`

Applying Pythagoras Theorem,

`KN^2+LN^2=KL^2`

Since LN=8:

`KN^2+8^2=KL^2`

`KN^2+8^2=(√(17+KN))^2`

KN=3.765