Answer:
- building: 222.61 ft
- flagpole: 32.15 ft
Step-by-step explanation:
The tangent function of an angle in a right triangle is the ratio of the opposite side to the adjacent side. Here, the adjacent side is 500 ft, so we have ...
tan(24°) = (building height)/(500 ft)
building height = (500 ft)tan(24°) ≈ 222.61 ft
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Similarly, the height to the top of the flagpole is ...
total height = (500 ft)tan(27°) ≈ 254.76 ft
The length of the flagpole is the difference of these heights:
flagpole length = 254.76 ft -222.61 ft = 32.15 ft
The height of the building is 222.61 ft; the length of the flagpole is 32.15 ft.
Answer:
![3\frac{2}{3} + 2\frac{2}{3} = 6\frac{1}{3}](https://tex.z-dn.net/?f=3%5Cfrac%7B2%7D%7B3%7D%20%2B%202%5Cfrac%7B2%7D%7B3%7D%20%3D%206%5Cfrac%7B1%7D%7B3%7D)
Step-by-step explanation:
Given
See attachment for number line
Required
Determine the model
From the attachment, we can see that each partition is 1/3
The gray rectangle covers 11 partitions.
So:
![Gray = 11 * \frac{1}{3}](https://tex.z-dn.net/?f=Gray%20%3D%2011%20%2A%20%5Cfrac%7B1%7D%7B3%7D)
![Gray = \frac{11}{3}](https://tex.z-dn.net/?f=Gray%20%3D%20%5Cfrac%7B11%7D%7B3%7D)
Express as a mixed number
![Gray = 3\frac{2}{3}](https://tex.z-dn.net/?f=Gray%20%3D%203%5Cfrac%7B2%7D%7B3%7D)
The black rectangle covers 8 partitions
So:
![Black= 8 * \frac{1}{3}](https://tex.z-dn.net/?f=Black%3D%208%20%2A%20%5Cfrac%7B1%7D%7B3%7D)
![Black= \frac{8}{3}](https://tex.z-dn.net/?f=Black%3D%20%5Cfrac%7B8%7D%7B3%7D)
Express as a mixed number
![Black= 2\frac{2}{3}](https://tex.z-dn.net/?f=Black%3D%202%5Cfrac%7B2%7D%7B3%7D)
So, the model is:
![Gray + Black = Total](https://tex.z-dn.net/?f=Gray%20%2B%20Black%20%3D%20Total)
Where Total is the point where the black rectangle stops
![3\frac{2}{3} + 2\frac{2}{3} = 6\frac{1}{3}](https://tex.z-dn.net/?f=3%5Cfrac%7B2%7D%7B3%7D%20%2B%202%5Cfrac%7B2%7D%7B3%7D%20%3D%206%5Cfrac%7B1%7D%7B3%7D)
Answer:
second one
Step-by-step explanation:
just read where the purple line finishes on the x axis, in this case it’s 5 so it’s greater than 5 or equal to it.
Answer:
c = 5
Step-by-step explanation:
- 6 + 2c = 3c -(6+5)
-6 + 2c = 3c -11
-6 + 11 = 3c- 2c
5 = c
Answer:
y=3
Step-by-step explanation:
this is because you are only given one number. And that is three.