Answer:
30.11 meters ( approx )
Step-by-step explanation:
Let x be the distance of a point P ( lies on the building ) from the top of the building such that AP is perpendicular to the building and y be the distance of the building from point A, ( shown in the below diagram )
Given,
Point A is 8.20 m above level ground,
So, the height of the building = ( x + 8.20 ) meters,
Now, 1 degree = 60 minutes,
⇒ ![1\text{ minute } =\frac{1}{60}\text{ degree }](https://tex.z-dn.net/?f=1%5Ctext%7B%20minute%20%7D%20%3D%5Cfrac%7B1%7D%7B60%7D%5Ctext%7B%20degree%20%7D)
![20\text{ minutes }=\frac{20}{60}=\frac{1}{3}\text{ degree}](https://tex.z-dn.net/?f=20%5Ctext%7B%20minutes%20%7D%3D%5Cfrac%7B20%7D%7B60%7D%3D%5Cfrac%7B1%7D%7B3%7D%5Ctext%7B%20degree%7D)
![50\text{ minutes }=\frac{50}{60}=\frac{5}{6}\text{ degree}](https://tex.z-dn.net/?f=50%5Ctext%7B%20minutes%20%7D%3D%5Cfrac%7B50%7D%7B60%7D%3D%5Cfrac%7B5%7D%7B6%7D%5Ctext%7B%20degree%7D)
By the below diagram,
![tan ( 12^{\circ} 50') = \frac{8.20}{y}](https://tex.z-dn.net/?f=tan%20%28%2012%5E%7B%5Ccirc%7D%2050%27%29%20%3D%20%5Cfrac%7B8.20%7D%7By%7D)
![tan(12+\frac{5}{6})^{\circ}=\frac{8.20}{y}](https://tex.z-dn.net/?f=tan%2812%2B%5Cfrac%7B5%7D%7B6%7D%29%5E%7B%5Ccirc%7D%3D%5Cfrac%7B8.20%7D%7By%7D)
![tan (\frac{77}{6})^{\circ}=\frac{8.20}{y}](https://tex.z-dn.net/?f=tan%20%28%5Cfrac%7B77%7D%7B6%7D%29%5E%7B%5Ccirc%7D%3D%5Cfrac%7B8.20%7D%7By%7D)
![\implies y=\frac{8.20}{tan (\frac{77}{6})^{\circ}}](https://tex.z-dn.net/?f=%5Cimplies%20y%3D%5Cfrac%7B8.20%7D%7Btan%20%28%5Cfrac%7B77%7D%7B6%7D%29%5E%7B%5Ccirc%7D%7D)
Now, again by the below diagram,
![tan (31^{\circ}20')=\frac{x}{y}](https://tex.z-dn.net/?f=tan%20%2831%5E%7B%5Ccirc%7D20%27%29%3D%5Cfrac%7Bx%7D%7By%7D)
![tan(31+\frac{1}{3})=\frac{x}{y}](https://tex.z-dn.net/?f=tan%2831%2B%5Cfrac%7B1%7D%7B3%7D%29%3D%5Cfrac%7Bx%7D%7By%7D)
![\implies x=y\times tan(\frac{94}{3})=\frac{8.20}{tan (\frac{77}{6})^{\circ}}\times tan(\frac{94}{3})^{\circ}=21.9142943216\approx 21.91](https://tex.z-dn.net/?f=%5Cimplies%20x%3Dy%5Ctimes%20tan%28%5Cfrac%7B94%7D%7B3%7D%29%3D%5Cfrac%7B8.20%7D%7Btan%20%28%5Cfrac%7B77%7D%7B6%7D%29%5E%7B%5Ccirc%7D%7D%5Ctimes%20tan%28%5Cfrac%7B94%7D%7B3%7D%29%5E%7B%5Ccirc%7D%3D21.9142943216%5Capprox%2021.91)
Hence, the height of the building = x + 8.20 = 30.11 meters (approx)
Is there more to this question or no?
Answer:
125.66 inches
Step-by-step explanation:
<u>Step 1: Calculate the circumference</u>
The circumference formula is: C = πd
Another way of saying that is: C = 2πr
C = 2π(20)
C = 40π
C ≈ 125.66 inches
Answer: 125.66 inches