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Ierofanga [76]
2 years ago
8

What is the length of the apothem of the regular pentagon shown below? Round to one decimal place

Mathematics
1 answer:
DerKrebs [107]2 years ago
7 0

Answer:

A

Step-by-step explanation:

Draw a diagonal line connecting the centre to a vertex at the bottom. This makes a triangle. It is a regular pentagon so the base of that triangle is 7.6 / 2, which is 3.8. You also know that the angle from the apothem to the base is 90 degrees. You also know that you could split the centre angle into 5 triangles. 360 / 5 = 72 and we have half of it so it is 36 degrees.

Let's see what we have so far:

The base of the triangle is 3.8

The angle at the bottom is 90

The angle at the top is 36

We now have the tan and the opposite and we need the adjacent so rearrange for adjacent.

This gives you adjacent = opposite / tan(angle)

adjacent = 3.8 / tan(36)

adjacent = 5.2m

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An opaque cylindrical tank with an open top has a diameter of 3.25 m and is completely filled with water. When the afternoon Sun
kicyunya [14]

Answer:

10.69

Step-by-step explanation:

We must first know that the angle of refraction is given by the following equation:

n_water * sin (A_water) = n_air * sin (A_air)

where n is the refractive index, for water it is 1.33 and for air it is 1.

The angle (A) in the air is 22.8 °, and that of the water is unknown.

Replacing these values we have to:

1.33 * sin (A_water) = 1 * 0.387

sin (A_water) = 1 * 0.387 / 1.33

A_water = arc sin (0.2907) = 16.9 °

now for the tank depth:

h = D / tan (A_water)

D = 3.25

Replacing

h = 3.25 / tan 16.9 °

h = 10.69

Therefore the depth is 10.69 meters.

6 0
3 years ago
I REALLY NEED HELP RIGHT NOW! T^T<br><br>Applying the 30-60-90 Theorem, Solve this.​
jarptica [38.1K]

Answer:

Step-by-step explanation:

take 30 degree as reference angle

using cos rule

cos 30=adjacent/hypotenuse

\sqrt{3}/2=7\sqrt{3}/y(do cross multiplication)

14\sqrt{3=y\sqrt{3}

14\sqrt3}/\sqrt{3}=y

14=y

for x

using pythagorsa theorem

H^2=P^2+B^2

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196=X^2+147

196-147=X^2

49=X^2

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6 0
3 years ago
I need help with my final, it’s my final grade
s2008m [1.1K]

Answer:

x=13

Step-by-step explanation:

14x-2=180

+2         +2

14x=182

/14       /14

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3 years ago
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6 0
3 years ago
Tanya walked for 171717 minutes from her home to a friend that lives 1.51.51, point, 5 kilometers away. d(t)d(t)d, left parenthe
Butoxors [25]

Correct question is;

Tanya walked for 17 minutes from her home to a friend that lives 1.5 kilometers away. D(t) models Tanyas remaining distance to walk in kilometers, t minutes since she left home. What number type is more appropriate for the domain of d?

Answer:

0 ≤ t ≤ 17 ; (0, 17)

Step-by-step explanation:

We are told that she has walked for 17 minutes from her home to a friend that lives 1.5 kilometers away.

Now, we want to find the domain of numbers that shows her remaining distance.

Since she spent 17 minutes, then it means in modeling remaining distance it could be from 0 to 17 minutes as the case may be. Thus, the domain can be written as;

0 ≤ t ≤ 17 ; (0, 17)

6 0
3 years ago
Read 2 more answers
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