SOLUTION: A funnel is placed on a glass as shown. If the glass is 12.5 cm tall and 8.2 cm in diameter, how high is the vertex of the funnel above the bottom of the glass? <img src="htt

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Question 1205071: A funnel is placed on a glass as shown. If the glass is 12.5 cm tall
and 8.2 cm in diameter, how high is the vertex of the funnel above the bottom
of the glass?

Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52754) About Me  (Show Source):
You can put this solution on YOUR website!
.

    how high is the vertex of the funnel above the bottom of the glass = 

    = 12.5 - 4.1%2Ftan%2828%5Eo%29 = 12.5 - 4.1%2F0.5317 = 4.79 cm  (rounded).     ANSWER

Solved.

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I think that everything is clear from the formula and calculations,
so, there is no need for more detailed explanations.



Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

View from the side


Let's split the smaller triangle down the middle.
This will bisect the 56 degree angle into two smaller 28 degree angles.


h = height of the triangle
8.2 cm is the diameter of the cylindrical glass, so 8.2/2 = 4.1 cm is the radius (and the horizontal leg of each right triangle).

tan(angle) = opposite/adjacent
tan(28) = 4.1/h
h = 4.1/tan(28)
h = 7.7109785 approximately

Subtract this from the height of the cylindrical glass to determine how far off the ground the vertex is
12.5 - 7.7109785 = 4.7890215

This then rounds to 4.8 cm when rounding to 2 sig figs. This is the lower sig fig count of 8.2 and 12.5
Round this value however your teacher instructs.