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Marizza181 [45]
2 years ago
5

Anna and Veronica are on the opposite sides of a tower of 160 meters height. They measure the angle of elevation of the top of t

he tower as 40° and 55° respectively. Find the distance between the two friends.
Mathematics
1 answer:
MAXImum [283]2 years ago
8 0

Answer: The distance between the girls is 362.8 meters.

Step-by-step explanation:

So we have two triangle rectangles that have a cathetus in common, with a length of 160 meters.

The adjacent angle to this cathetus is 40° for Anna, then the opposite cathetus (the distance between Anna and the tower) can be obtained with the relationship:

Tan(A) = opposite cath/adjacent cath.

Tan(40°) = X/160m

Tan(40°)*160m = 134.3 m

Now, we can do the same thing for Veronica, but in this case the angle adjacent to the tower is 55°

So we have:

Tan(55°) = X/160m

Tan(55°)*160m = X = 228.5 m

And we know that the girls are in opposite sides of the tower, so the distance between the girls is equal to the sum of the distance between each girl and the tower, then the distance between the girls is:

Dist = 228.5m + 134.3m = 362.8m

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In 2012, California had a population of about 38 million people, and North Dakota had a population of about 699,000 people. What
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Answer:

37,301,000

Step-by-step explanation:

The difference in population can be determined by subtracting the population of North Dakota from California

38,000,000 - 699,000 = 37,301,000

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Find the exact value for cos π 12 applying sum and difference formulas involving π 3 and π 4 .
nadya68 [22]

First, split the angle into two angles where the values of the six trigonometric functions are known. In this case, π/12 can be split into π/3−π/4.

cos(π/3−π/4)

Use the difference formula for cosine to simplify the expression. The formula states that cos(A−B)=cos(A)cos(B)+sin(A)sin(B)

cos(π/3)⋅cos(π/4)+sin(π/3)⋅sin(π/4)

The exact value of cos(π/3) is 12, so:

(12)⋅cos(π/4)+sin(π/3)⋅sin(π/4)

The exact value of cos(π/4) is √22.

(12)⋅(√22)+sin(π/3)⋅sin(π/4)

The exact value of sin(π/3) is √32.

(12)⋅(√22)+(√32)⋅sin(π/4)

The exact value of sin(π/4) is √22.

(12)⋅(√22)+(√32)⋅(√22)

Simplify each term:

√24+√64

Combine the numerators over the common denominator.

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Maya bought a dozen specialty donuts at the bakery for $18. She purchased a mixture of frosted donuts for $2 each, glazed donuts
Zina [86]

Answer:

The quantity of frosted donuts = 2

The quantity of glazed donuts = 9

The quantity of custard filled donuts = 1

Step-by-step explanation:

Let the quantity of frosted donuts = x

Let the quantity of glazed donuts = y

Let the quantity of custard filled donuts = z

As per question statements, following equations can be made:

x+y+z=12......(1)\\2x+y+5z=18.....(2)\\x=2z ...... (3)

Putting x=2x in (1) and (2):

y+3z=12 .... (4)\\y+9z=18 .... (5)

Subtracting (4) from (5):

6z=6\\\Rightarrow z =\bold{1}

By equation (3):

x=\bold{2}

By equation (1):

y=\bold{9}

Therefore, the answers are:

The quantity of frosted donuts = 2

The quantity of glazed donuts = 9

The quantity of custard filled donuts = 1

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2 years ago
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