What is the measure of the height of triangle KLO.? L8cmM,M4.5cmN,O13cmN,KO,KL.?

To find the height of triangle KLO, we need to first determine which side is the base and which side is the height. In this case, it seems like the side KO is the base and the side KL is the height.

Using the Pythagorean theorem, we can find the height of triangle KLO:

KL^2 = KO^2 - LO^2
KL^2 = 13^2 - 8^2
KL^2 = 169 - 64
KL^2 = 105
KL = √105
KL ≈ 10.25 cm

Therefore, the height of triangle KLO is approximately 10.25 cm.

The height of triangle KLO is 6 cm.

Explanation:
The height of a triangle is the perpendicular distance from a vertex to the opposite side. In this case, the height of triangle KLO is the distance from vertex K to side LO.

To find the height, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the hypotenuse is KO, and the other two sides are KL and LO. We know that KO = 13 cm and KL = 8 cm.

Using the Pythagorean theorem, we can find LO:

LO^2 = KO^2 - KL^2
LO^2 = 13^2 - 8^2
LO^2 = 169 - 64
LO^2 = 105
LO = √105
LO = 10.25 cm

Now that we know LO, we can use the formula for the height of a triangle:

height = (1/2) - base - height
height = (1/2) - KL - LO
height = (1/2) - 8 cm - 10.25 cm
height = 41 cm
height = 6 cm

Therefore, the height of triangle KLO is 6 cm.