SOLUTION: A bowl is filled with water to a depth of x cm. Point C is the midpoint of the diameter of the bowl. Triangle ABC is equilateral with sides 10cm. Find the value of x, in cm. Dia

Question 1148119: A bowl is filled with water to a depth of x cm. Point C is the midpoint of the diameter of the bowl. Triangle ABC is equilateral with sides 10cm. Find the value of x, in cm.
Diagram: https://imgur.com/a/RuDZ8ou
COULD YOU PLEASE EXPLAIN STEP BY STEP AND NOT JUMP TO THE ANSWER/CONCLUSION. THANKS

Found 2 solutions by Alan3354, Theo:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Step 1, find the altitude of the equilateral triangle with sides of 10 cm.
Call it h.
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Step 2, subtract h from 10.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the bowl is a semi-circle, so it seems.
the triangle is equilateral with sides of 10 cm each.
point C is half the distance of the diameter.
that makes the radius of the semi-circle equal to 10 cm.
my diagram is shown here:

since CE, in my diagram, is also the radius of the semi-circle, then CE is also equal to 10 cm.
BCD forms a right triangle.
since triangle ABC is equilateral, then:
angle BAC = 60 degrees.
angle CAB = 60 degrees.
angle ABC = 60 degrees.
since CD is perpendicular to AC, then angle ACD is equal to 90 degrees.
this makes angle BCE equal to 30 degrees because angle ACE is equal to angle ACB plus angle BCE.
triangle BCD is a right 30-60-90 degree triangle.
the side opposite the 60 degree angle is equal to sqrt(3) / 2 * the length of the hypotenuse.
the length of the hypotenuse is 10.
that makes the length of CD equal to (sqrt(3)/2) * 10 = 8.660254038
since the length of CE is 10, then x must be equal to 10 - 8.660254038 = 1.339745962.
you can also verify with trigonometry to find the length of CD.
sin(60) = opposite / hypotenuse = CD / 10
solve for CD to get CD = 10 * sin(60) = 8.660254038.
the trigonometry confirms the geometry, so the length of CD looks to be correct.
that confirms that the length of CE is also correct.

i didn't solve this for you earlier, but the problem intrigued me so i ventured a solution.
hopefully the solution i arrived at agrees with the previous solution you were given.

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