The Eiffel Tower in Paris, France. Lizbeth is 5.5 feet tall. She looks up at an angle of elevation of 72° to see the top from 31
1 answer:
Answer:
The height of the Eiffel Tower will be 318 feet.
Step-by-step explanation:
Please check the attached graph.
From the diagram, it is clear that Lizbeth is 5.5 ft tall, seeing the top from 318 feet away, making an angle of elevation to be 72⁰.
The diagram makes a right-angled triangle.
- Given the angle = Ф = 72⁰
- Adjacent = a = 5.5 ft
- Opposite = b = 318 ft
- Hypotenuse = the height of the Eiffel Tower = c ?
Pythagorean Theorem:
For a right-angled triangle, with sides 'a' and 'b', the hypotenuse 'c' is defined as:
feet
Therefore, the height of the Eiffel Tower will be 318 feet.
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Answer:
165 different teams of 3 students can be formed for competitions
Step-by-step explanation:
Combinations of m elements taken from n in n (m≥n) are called all possible groupings that can be made with the m elements so that:
- Not all items fit
- No matter the order
- Elements are not repeated
That is, a combination is an arrangement of elements where the place or position they occupy within the arrangement does not matter. In a combination it is interesting to form groups and their content.
To calculate the number of combinations, the following expression is applied:
It indicates the combinations of m objects taken from among n objects, where the term "n!" is called "factorial of n" and is the multiplication of all the numbers that go from "n" to 1.
In this case:
- n: 3
- m: 11
Replacing:
Solving:
being:
- 3!=3*2*1=6
- 8!=8*7*6*5*4*3*2*1=40,320
- 11!=39,916,800
So:
C= 165
<u><em>165 different teams of 3 students can be formed for competitions</em></u>