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Papessa [141]
3 years ago
12

The flagpole in front of CB East casts a shadow 40 feet long when the measurement of the angle of elevation to the sun is 31˚. H

ow tall is the flagpole?

Mathematics
1 answer:
IRINA_888 [86]3 years ago
5 0

Answer: The length of flagpole is 24 feet.

Step-by-step explanation:

Since we have given that

Length of shadow =40 feet

Angle of elevation to the sun = 31\textdegree

In ΔABC,

We can apply "trigonometric rules ",

\tan\theta=\frac{AB}{BC}\\\\\tan31\textdegree=\frac{AB}{40}\\\\0.6\times 40=AB\\\\24\ feet=AB

Hence, the length of flagpole is 24 feet.

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There is a crab on the ocean for 60 feet below sea level in a bird 120 feed in the air. how far apart are the crab in the bird?
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The answer is the crab and the bird are 180 feet apart
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3 years ago
Find the area of the given triangle to the nearest square unit. Angle a= 30 degrees, b=10, angle B=45 degrees
storchak [24]

Answer:

A=34\ units^2

Step-by-step explanation:

Suppose we have a general triangle like the one shown in the figure.

We know the angle A, the angle B and the length b.

A = 30\°\\\\B = 45\°\\\\b = 10

By definition I know that the sum of the internal angles of a triangle is always equal to 180 °.

So

A + B + C = 180\\\\30 + 45 + C = 180

We solve the equation and thus we find the angle C.

C = 180 - 30-45\\\\C = 105

We already know the three triangle angles.

Now we use the sine theorem to calculate the sides c and a.

The  sine theorem says that:

\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}

Then

\frac{sin(30)}{a}=\frac{sin(45)}{10}

\frac{sin(30)}{\frac{sin(45)}{10}}=a

a=7.071

Also

\frac{sin(105)}{c}=\frac{sin(45)}{10}

\frac{sin(105)}{\frac{sin(45)}{10}}=c

c=13.660

Finally, we use the Heron formula to calculate the triangle area

A=\sqrt{s(s-a)(s-b)(s-c)}

Where s is:

s=\frac{a+b+c}{2}

Therefore

s=\frac{7.071+10+13.660}{2}

s=15.37

A=\sqrt{15.37(15.37-7.071)(15.37-10)(15.37-13.66)}

A=34\ units^2

3 0
3 years ago
An obtuse triangle has a side length of $16,$ and a side length of $21.$ The third side length is also a positive integer. How m
Ymorist [56]

Answer:

3

Step-by-step explanation:

3 0
3 years ago
What is the value of x in x2-3x=28
charle [14.2K]

Answer:

x=-28

Step-by-step explanation:

2x-3x=-1x so if -1x=28 divide both sides by -1 so x= -28

5 0
3 years ago
Use the geometric mean to find the 7th term in a geometric sequence if the 6th term is 12 and the 8th term is 27. 20 19.5 18 17
Lesechka [4]
A₆ =12

a₇ = ?? = x

a₈ 27

In this case x is the geometric mean & as per the formula
geometric mean of 2 numbers =√(a₆ * a₈) = √(12*27)
& x=18.
Proof:
Find the common ratio between a₇ & a₆ ==> = ( x) / 12
now find the common ration between a₈ & a₇ ===> =27 / (x)
x/12 = 27/x ===> x² = 12*27 ==> x² = 324 & x =√324 = 18
7 0
3 years ago
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