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agasfer [191]
3 years ago
10

Central Boulevard runs diagonally across town as shown below. The distance from Eastern Avenue to Western Avenue along South Str

eet is 4(sqrt)3 miles.
Mathematics
1 answer:
murzikaleks [220]3 years ago
5 0
The locations of the streets describes a right triangle with the angles 30 degrees and 60 degrees between them and the length of the side opposite the 60 degrees angle is 4\sqrt{3} \, miles

a.) To find the distance form North Street to South Street along Eastern Avenue, we find the length of the side opposite the 30 degrees angle.

Using sine rule, we recall that the sine rule states that
\frac{\sin{A}}{a} = \frac{\sin{B}}{b}
where:
a = 4\sqrt{3}
A = 60 degrees
B = 30 degrees
b = unknown
\frac{\sin{60^o}}{4\sqrt{3}} = \frac{\sin{30^o}}{b} \\ b=\frac{4\sqrt{3} \sin{30^o}}{\sin{60^o}}= \frac{3.4641}{0.8660} = 4 \, miles

Therefore, the distance form North Street to South Street along Eastern Avenue is 4 miles.

b.) To find the distance from North Street to South Street along Central Boulevard we find the length of the hypothenus of the right triangle.

Using pythagoras theorem, we recall that the pythagoras states that
c^2=a^2+b^2
where:
a = 4\sqrt{3}
b = 4 miles
c = hypothenus = unknown
c^2=\left(4 \sqrt{3} \right)^2+4^2=48+16=64 \\ c= \sqrt{64} =8 \, miles

Therefore, the distance from North Street to South Street along Central Boulevard is 8 miles
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ryzh [129]

angle 3 and angle 4 are adjacent and complementary.

angle 5 is a vertical angle to the combination of angle 3 and 2

angle 4 and angle 5 are adjacent, supplementary, and form a linear pair

If you want me to explain why, comment it, i just have no time to now.

6 0
3 years ago
A weather report said there is a 60% chance of rain on Monday, and a 30% chance of rain on Tuesday. Based on the report, what is
sergey [27]

Answer:

The answer is 18 percent, or 9/50.

Step-by-step explanation:

We first convert the chance of rain on Monday into a fraction.

60%=60/100=3/5.

We then convert the chance of rain on Tuesday into a fraction.

30%=30/100=3/10.

Because the two events are independent(i.e. If it rains on Tuesday doesn't depend on if it rains on Monday) we multiply them together to get the probability they both happen. That chance is:

3/5 * 3/10=(3*3)/(5*10)=9/50(fraction form)=18/100=18%(percent form)

5 0
2 years ago
Express 84,42 as a percentage of 74,05 rounded off to a whole number
Leto [7]
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5 0
3 years ago
PLEASE HELP
BigorU [14]
Try substituting some values in, and you will get your answer.

I'll do the first two.

y = (0) + 4 [=4]
y = (2) + 4 [=6]

In the table, the first two values for y are 6 and 8.
The first two values for y = x + 4 are 4 and 6.

Therefore, we can assume that the rate of change in the function y = x + 4 is less than the rate of change of the function represented in the table.

7 0
3 years ago
Read 2 more answers
In circle D, if the measure of arc Gec is 230 , what is the measure of minor arc GFC
BabaBlast [244]

Answer:

The measure of minor arc GFC is 130\°

Step-by-step explanation:

we know that

In a circle the sum of the major arc plus the minor arc is equal to 360 degrees

see the attached figure to better understand the problem

Let

x------> the major arc GEC

y-----> the minor arc GFC

so

x+y=360\°

we have

x=230\°

substitute in the equation and solve for y

230\°+y=360\°

y=360\°-230\°=130\°

8 0
3 years ago
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