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MakcuM [25]
2 years ago
5

When she is outdoors, Tasha the dog, is tied to a stake in the center of a circular area of radius 24 feet. The angle between he

r dog bourse and her favorite hydrant is 65 degrees. What is the length of the arc from her dog house to the hydrant, following minor arc DG, to the nearest foot.

Mathematics
1 answer:
Vlad [161]2 years ago
3 0

Answer: the length of the arc from her dog house to the hydrant is 69 feet

Step-by-step explanation:

The formula for determining the length of an arc is expressed as

Length of arc = θ/360 × 2πr

Where

θ represents the central angle.

r represents the radius of the circle.

π is a constant whose value is 3.14

From the information given,

Radius, r = 24 feet

θ = 165 degrees

Therefore,

Length of the minor arc, DG = 165/360 × 2 × 3.14 × 24

Length of arc = 69 feet rounded up to the nearest feet.

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A kite is stuck in a 36-ft tree. If the angle of elevation from the kite and the ground is 12, find the length of the kite.
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Answer:

173.15 ft.  

Step-by-step explanation:

Please find the attachment.

Let L be the length of kite.  

We have been given that a kite is stuck in  36-ft tree. The angle of elevation from the kite and the ground is 12.

We can see from our attachment that kite and tree form a right triangle. height of tree is opposite of angle of elevation and length of kite is hypotenuse.

Since we know that Sine relates the opposite and hypotenuse of a right triangle, so we will use sine to find the length of kite.

sin(12)=\frac{36}{L}    

L=\frac{36}{sin(12)}

L=\frac{36}{0.207911690818}  

L=173.1504364105882792\approx 173.15

Therefore, the length of kite is 173.15 ft.

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Adult men have heights with a mean of 69. 0 inches and a standard deviation of 2. 8 inches. find the z-score of a man who is 71.
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The value of the z score is 1.03.

According to the statement

we have given that the value of mean and standard deviation and we have to find the value of the z score.

So, For this purpose we know that the

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