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PIT_PIT [208]
3 years ago
12

Find the measure of the angle formed between the base of the cone and a line segment that represents the slant height.

Mathematics
1 answer:
Natali [406]3 years ago
6 0
Remark.
Thank you for the clear diagram. You need to find AB somehow. When you do you can find the desired angle by using the inverse tan.

Step One
Find AB
AB = the radius of the cone
AB = 1/2 the diameter of the cone
AB = 1/2 * 4
AB = 2 inches.

Step two
Determine The Tangent of the desired angle
Tan(A) = opposite of adjacent
opposite side = h = 6 inches
Adjacent = AB = radius = 2 inches.

Tan(A) = 6/2 = 3 

Step 3
Find the inverse Tan
A = inverse Tan(A)
A =  inverse Tan(3)
A = 71.57 degrees <<<<< Answer.

There are other ways of finding the angle you want, but I think this is the quickest.
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Explanation:

1) given

Table:

<span>Altitude (in thousands of feet)    Boiling Point of Water (Fahrenheit)

(sea level) 0                                212
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2) The independent variable is the input of the function, and the dependent variable is the output of the function.

The input determines the output once the rule is established.

Therefore:

a) the independent variable is the altitude, and
b) the dependent variable is the boiling point of water in Farenheit.

3) The slope of the graph would be:

                 change in the dependent variable          change in boiling point
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Therefore, the slope represents the average change in the boiling boilin point of water every one thousand feet on change of altitude.

If the relationship is not linear, then the slope is not constant, and you will have different slopes for different parts.

If the slope is negative, means that as the altitude increase the boiling point of water decrease.

You can calculate the slope using any two pair of points (data)

              212 - 210           2
slope =---------------- =   ------- = - 2
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or, using other pair of points:

                204.8 - 210           -5.2             
slope = --------------------- =   --------- = -2.6
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As you see, the slope is not constant. So, the function is not linear.
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