Geometry help, please & thank you!?

Question

PM is an altitude of equilateral triangle PKO. If PK=4, find PM.

Answer 1

All sides have the same measurement in the triangle, 4. PM intersects one of the sides exactly 1/2 the distance so the new triangle it makes has MO=2 (or MK if you prefer). The same is true for the angles, angle P is 30, angle O is 60 and angle M is 90.

You don't need the angles unless you are doing the answer as a trig function but if you want to use the formula A^2 + B^2 = C^2 you can find the answer too, where C is PK.

(PM)^2 + (MO)^2 = (PK)^2

(PM)^2 + 2^2 = 4^2

(PM)^2 + 4 = 16

(PM)^2 = 16 - 4

SqR[(PM)^2] = SqR (12) [where SqR is Square Root]

PM = 3.4641016151377545870548926830117

Answer 2

Because you have an equilateral triangle, then the measure of each side is 4. Also because you have an equilateral triangle, the altitude splits the triangle in half giving you two right triangles with bases on 2. Now you can use the Pythagorean theorem to find the altitude, or the altitude
a^2+b^2=c^2
a^2+2^2=4^2
a^2+4=16
a^2=12
a=sqrt 12
a=2 root 3 or a=3.464

I hope this helps

Answer 3

If you draw a picture, you will see that segment PM is one of the legs of a right triangle which has a hypotenuse of 4 units and an adjacent leg of 2 units. That means you can find the measure of PM with the Pythagorean Theorem. Here are the steps:
2^2 + x^2 = 4^2
4 + x^2 = 16
x^2 = 12
sqrt(x^2) = sqrt(12)
x = sqrt(2 * 2 * 3)
x = 2 * sqrt(3)

Answer 4

since it is an equilateral triangle then you can easily use the pythagorean theorem to solve this:

a^2+b^2=c^2

a is 4/2 because its a equilateral triangle that means the altitude cuts the midpoint of the base

2^2+b^2=4^2
b^2=16-4
b=sqrt(12)
b=2root3
therefore pm is 2root3

Answer 5

If all sides is 4, then to find the height of PM use the A-square + B-square = C-square. Where PM would be B, then the base would be 2-square(4)and C would be 4-square(16).

B-square = 16 - 4
B-square = 12
the square of 12 is ???

can't do it all for you.

Answer 6

PK = OP = OK = 4
then OM = MK = 2
(PM)^2 + (MK)^2 = (PK)^2
by poor old Pythagorus,
PM = sqr[(PK)^2 - (MK)^2] = sqr[ 4^2 - 2^2] = sqr[ 16-4]
= sqr[4*3] = 2sqr[3]