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JulijaS [17]
3 years ago
10

If the short leg of a 30-60-90 triangle is 6, approximately how long is the hypotenuse?

Mathematics
1 answer:
Y_Kistochka [10]3 years ago
6 0

Answer:

12

Step-by-step explanation:

In a triangle, shortest side has the shortest angle opposite to it.

As 6 is the shortest side angle opposite to it is 30.

Let the hypotenuse be h.

h*sin(30) = 6

h*(1/2) = 6

h = 12

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Make a histogram, using a bin width of ten, to display the bowling scores for these 31 players: 87, 104, 79, 94, 117, 82, 72, 11
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Step-by-step explanation:

Using R, I used the following code to create a histogram:

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data.frame(bowling.scores)

ggplot(data.frame(bowling.scores), aes(x=bowling.scores)) +  

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7 0
2 years ago
What is one way that oak trees can spread to different areas
crimeas [40]
By dropping acorns, and spreading them to other areas by animals and wind.
7 0
3 years ago
Read 2 more answers
A plane flying horizontally at an altitude of 3 miles and a speed of 500 mi/h passes directly over a radar station. Find the rat
konstantin123 [22]

Answer:

The rate at which the distance from the plane to the station is increasing is 331 miles per hour.

Step-by-step explanation:

We can find the rate at which the distance from the plane to the station is increasing by imaging the formation of a right triangle with the following dimensions:

a: is one side of the triangle = altitude of the plane = 3 miles

b: is the other side of the triangle = the distance traveled by the plane when it is 4 miles away from the station and an altitude of 3 miles

h: is the hypotenuse of the triangle = distance between the plane and the station = 4 miles                    

First, we need to find b:    

a^{2} + b^{2} = h^{2}   (1)    

b = \sqrt{h^{2} - a^{2}} = \sqrt{(4 mi)^{2} - (3 mi)^{2}} = \sqrt{7} miles

Now, to find the rate we need to find the derivative of equation (1) with respect to time:

\frac{d}{dt}(a^{2}) + \frac{d}{dt}(b^{2}) = \frac{d}{dt}(h^{2})

2a\frac{da}{dt} + 2b\frac{db}{dt} = 2h\frac{dh}{dt}

Since "da/dt" is constant (the altitude of the plane does not change with time), we have:  

0 + 2b\frac{db}{dt} = 2h\frac{dh}{dt}

And knowing that the plane is moving at a speed of 500 mi/h (db/dt):

\sqrt{7} mi*500 mi/h = 4 mi*\frac{dh}{dt}

\frac{dh}{dt} = \frac{\sqrt{7} mi*500 mi/h}{4 mi} = 331 mi/h  

Therefore, the rate at which the distance from the plane to the station is increasing is 331 miles per hour.

I hope it helps you!

4 0
2 years ago
Find the distance between each pair of parallel line<br>y=x-6 and y=x+8
myrzilka [38]
Both these lines are linear and have the same slope, just different y-intercepts. This means one line is shifted higher than the other. y=x+8 is 14 units higher than y=x-6. The answer to you question therefore is 14 units!
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2 years ago
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