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tia_tia [17]
2 years ago
12

What is the exact value of the cos F?

Mathematics
1 answer:
Galina-37 [17]2 years ago
7 0

Answer:

cos(F) = 9/41

Step-by-step explanation:

The triangles are similar, so you know that ...

... cos(D) = cos(A) = 40/41.

From trig relations, you know ...

... cos(F) = sin(D)

and

... sin(D)² +cos(D)² = 1

So ...

... cos(F) = sin(D) = √(1 -cos(D)²) = √(1 -(40/41)²) = √(81/1681)

... cos(F) = 9/41

_____

The ratio for cos(A) tells you that you can consider AB=40, AC=41. Then, using the Pythagorean theorem, you can find BC = √(41² -40²) = √81 = 9.

From the definition of the cosine, you know cos(C) = BC/AC = 9/41. Because the triangles are similar, you know

... cos(F) = cos(C) = 9/41

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An architect designs a castle tower for a new attraction at a popular amusement park. Blueprints of the tower, which is in the s
marin [14]

Answer:

<u>The surface area of the tower is 5,218.1 m²</u>

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Height of the blueprint = 47 cm

Length of the blueprint = 23 cm

Width of the blueprint = 25 cm

Scale factor 1 : 96

2. Calculate the actual surface area of the tower and enter your answer in square meters with two decimal places.

Let's calculate the measurements of the actual tower:

Height of the blueprint = 47 * 96 = 4,512 cm = 45.12 m

Length of the blueprint = 23 * 96 = 2,208 cm = 22.08 m

Width of the blueprint = 25 * 96 = 2,400 cm = 24 m

Now, let's calculate the surface area of the tower, this way:

Surface area of the tower = 2* (24 * 22.08) + 2 * (45.12 * 22.08) + 2 * (45.12 * 24)

Surface area of the tower = 1,059.84 + 1,992.5 + 2,165.76

<u>Surface area of the tower = 5,218.1 m²</u>

4 0
2 years ago
Carey is organizing her books and putting them on
Aleksandr [31]
They are multiplying by 4 each set of numbers
5 0
2 years ago
In a second grade class containing 13 girls and 10 boys, 2 students are selected at random to give out the math papers. what is
Natali5045456 [20]
The fact that the first chosen student was a girl is already decided, so there is no need to find the probability of that happening. There are a total of 13+10, or 23 students. A girl was already selected, so that leaves 22 students. The chance that a boy is chosen is 10/22, or 5/11.
4 0
2 years ago
Determine whether a triangle can be formed with the given side lengths. If so, use Heron's formula to find the area of the trian
AfilCa [17]

Answer:

Triangle inequality rule states that the sum of eachpair of sides must be greater than the third sides.

240 + 123 > 207 true

240 + 207 > 123 true

123 + 207 > 240 true

A = √(s(s-a)(s-b)(s-c))

s is the semi-perimeter (a + b + c)/2

s = (240 + 123 + 207)/2

s = 285

A = √(285*(285-249)(285-123)(285-207))

A = 12,730 units^2

Step-by-step explanation:

4 0
1 year ago
One morning, eight buses arrive at a bus stop.
Semenov [28]

Answer:

0 and 5 minutes

Step-by-step explanation:

Median is the middle observation of given data. It can be found by following steps:

Arranging data in ascending or descending order.

Taking the average of middle two value if the total number of observation is even, and this average is our median.

or, if we odd number of observation then the most middle value is our median.

The mode is the observation which has a high number of repetitions (frequency).

We have given 8 numbers and we have to find the other two numbers a minute late for each bus to arrive at the bus stop.

Also, we have given the median and mode of all 10 buses i.e. 3.5 and 0 respectively.

Since the mode is 0, so the frequency of 0 must be greater than 2 times and less than or equal to 4 times.

The frequency of 0 is 4 is not possible as then we didn't get a median 3.5 then.

So the frequency of 0 is 3.

Hence one of number is 0 in two unknown number of a minute late for each bus arrive at the bus stop.

Now, we have the number of minutes late for each bus after arranging them in ascending order is: 0 0 0 2 2 6 8 8 9

For getting a median 3.5 we must have a number between 2 and 6. Let it be x then:

\frac{2+x}{2} = 3.5

⇒x = 5

Hence the number of minutes late for each bus is: 0 0 0 2 2 5 6 8 8 9

Thus, 0 and 5 are minutes late for the two-afternoon buses.

6 0
2 years ago
Read 2 more answers
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