Question

Find the missing lengths: LO=5 and OK=4, find OH and KH.

Answer 1

Answer:

The length of KH is 6 units and OH is 6.3 units.

Step-by-step explanation:

Given the figure with lengths LO=5 and OK=4. we have to find the length of  OH and KH.

In ΔLOH

By Pythagoras theorem

$LH^2=LO^2+OH^2\\\\LH^2=5^2+OH^2$ → (1)

In ΔKOH,

$KH^2=OH^2+OK^2\\\\KH^2=OH^2+4^2$  → (2)

In ΔKHL,

$KL^2=LH^2+KH^2$

Using eq (1) and (2), we get

$KL^2=5^2+OH^2+OH^2+4^2$

$9^2=25+2OH^2+16$

⇒ $2OH^2=81-25-16=40$

⇒ $OH=\sqrt{20}=6.324\sim6.3units.$

Put the above value in eq 2, we get

$KH^2=20+4^2=36$

⇒ KH=6 units.

Answer 2

Answer:

KH = 6, OH = $\sqrt{20}$

Step-by-step explanation:

Just Cause