Answer:
The height is 3791 ft.
Step-by-step explanation:
You need to make a drawing. Start with a vertical segment, 2 inches long, on the left side of the page. Label the top point A and the bottom point B. At the bottom endpoint, draw a longer horizontal segment, 4 inches long, to the right. Label the bottom right endpoint C. Connect A and C with a segment. Angle C is the original angle of elevation. On the bottom horizontal side, approximately 1 inch to the left of C, draw point D. Connect D and A with a segment. DA = 1000 ft. m<C = 34.8°. m<ABD = 40.4°. We are looking for AB, the height of the volcano.
We can work on triangle ADC.
m<C = 34.8°
Angles ADB and ADC are a linear pair, so m<ADC = 180° - 40.4° = 139.6°
m<DAC + m<ADC + m<C = 180°
m<DAC + 139.6° + 34.8° = 180°
m<DAC = 5.6°
Using the law of sines, we can find AC.
![\dfrac{\sin A}{a} = \dfrac{\sin B}{b}](https://tex.z-dn.net/?f=%20%5Cdfrac%7B%5Csin%20A%7D%7Ba%7D%20%3D%20%5Cdfrac%7B%5Csin%20B%7D%7Bb%7D%20)
![\dfrac{\sin 5.6^\circ}{1000} = \dfrac{\sin 139.6^\circ}{AC}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csin%205.6%5E%5Ccirc%7D%7B1000%7D%20%3D%20%5Cdfrac%7B%5Csin%20139.6%5E%5Ccirc%7D%7BAC%7D)
![AC = \dfrac{1000\sin 139.6^\circ}{\sin 5.6^\circ}](https://tex.z-dn.net/?f=AC%20%3D%20%5Cdfrac%7B1000%5Csin%20139.6%5E%5Ccirc%7D%7B%5Csin%205.6%5E%5Ccirc%7D)
![AC = 6642~ft](https://tex.z-dn.net/?f=%20AC%20%3D%206642~ft%20)
Now we use triangle ABC. AC = hypotenuse. AB = opposite leg. <C is known angle.
![\sin C = \dfrac{opp}{hyp}](https://tex.z-dn.net/?f=%20%5Csin%20C%20%3D%20%5Cdfrac%7Bopp%7D%7Bhyp%7D%20)
![\sin 34.8^\circ = \dfrac{AB}{6642~ft}](https://tex.z-dn.net/?f=%5Csin%2034.8%5E%5Ccirc%20%3D%20%5Cdfrac%7BAB%7D%7B6642~ft%7D)
![AB = 6642~ft \times \sin 34.8^\circ](https://tex.z-dn.net/?f=AB%20%3D%206642~ft%20%5Ctimes%20%5Csin%2034.8%5E%5Ccirc)
![AB = 3791~ft](https://tex.z-dn.net/?f=%20AB%20%3D%203791~ft%20)
Answer: The height is 3791 ft.
Answer:
the answer is 45 please do you get it
Answer:
3
Step-by-step explanation:
because it is the largest degree
Answer:
The will be 27000 bacteria in 36 hours from the start of the experiment
Step-by-step explanation:
In the first 18 hours:
The number of bacteria grew from 30 to 900.
So it grew by a factor of 900/30 = 30.
36 hours from the start of the experiment:
That is, the next 18 hours.
It will also grow by a factor of 30.
From 900 to 900*30 = 27000
The will be 27000 bacteria in 36 hours from the start of the experiment