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gulaghasi [49]
3 years ago
10

A tree struck by lightning in a storm breaks and falls over to form a triangle with the ground. The tip of the tree makes a 36°

angle with the ground 25 ft from the base of the tree. What was the height of the tree to the nearest foot?

Mathematics
1 answer:
liraira [26]3 years ago
5 0

Answer: approximately 49 feets

Step-by-step explanation:

The diagram of the tree is shown in the attached photo. The tree fell with its tip forming an angle of 36 degrees with the ground. It forms a right angle triangle,ABC. Angle C is gotten by subtracting the sum of angle A and angle B from 180(sum of angles in a triangle is 180 degrees).

To determine the height of the tree, we will apply trigonometric ratio

Tan # = opposite/ adjacent

Where # = 36 degrees

Opposite = x feets

Adjacent = 25 feets

Tan 36 = x/25

x = 25tan36

x = 25 × 0.7265

x = 18.1625

Height of the tree from the ground to the point where it broke = x = 18.1625 meters.

The entire height of the tree would be the the length of the fallen side of the tree, y + 18.1625m

To get y, we will use Pythagoras theorem

y^2 = 25^2 + 18.1625^2

y^2 = 625 + 329.88

y^2 = 954.88

y = √954.88 = 30.9 meters

Height of the tree before falling was

18.1625+30.9 = 49.0625

The height of the tree was approximately 49 feets

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krek1111 [17]

Answer:

The test statistic for the appropriate test is \frac{0.15-0.275}{\sqrt{0.2125(1-0.2125)[\frac{1}{40}+\frac{1}{40}]}}.

Step-by-step explanation:

The experiment conducted here is to determine whether there is a difference in proportion of starfish over 8 inches in length in the two ocean areas, i.e. north and south.

The hypothesis to test this can be defined as follows:

<em>H₀</em>: There is no difference in proportion of starfish over 8 inches in length in the two ocean areas, i.e. <em>p</em>₁ = <em>p</em>₂.

<em>Hₐ</em>: There is a difference in proportion of starfish over 8 inches in length in the two ocean areas, i.e. <em>p</em>₁ ≠ <em>p</em>₂.

The two-proportion <em>z</em>-test would be used to perform the test.

A sample of <em>n</em> = 40 starfishes are selected from both the ocean areas.

It provided that of the 40 starfish from the north, 6 were found to be over 8 inches in length and of  the 40 starfish from the south, 11 were found to be over 8 inches in length.

Compute the sample proportion of starfish from north that were over 8 inches in length as follows:

\hat p_{n}=\frac{6}{40}=0.15

Compute the sample proportion of starfish from south that were over 8 inches in length as follows:

\hat p_{s}=\frac{11}{40}=0.275

The test statistic is:

z=\frac{\hat p_{n}-\hat p_{s}}{\sqrt{P(1-P)[\frac{1}{n_{n}}+\frac{1}{n_{s}}]}}

Compute the combined proportion <em>P</em> as follows:

P=\frac{X_{n}+X_{s}}{n_{n}+n_{s}}=\frac{6+11}{40+40}=0.2125

Compute the test statistic value as follows:

z=\frac{\hat p_{n}-\hat p_{s}}{\sqrt{P(1-P)[\frac{1}{n_{n}}+\frac{1}{n_{s}}]}}

  =\frac{0.15-0.275}{\sqrt{0.2125(1-0.2125)[\frac{1}{40}+\frac{1}{40}]}}

Thus, the test statistic for the appropriate test is \frac{0.15-0.275}{\sqrt{0.2125(1-0.2125)[\frac{1}{40}+\frac{1}{40}]}}.

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1st find out how much the tip was:
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Now find the percentage 13.5 is of 75
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I think the calculation answer will be 9,999,811,112

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