For this case we have that the area of the triangle is given by:
![A = \frac {b * h} {2}](https://tex.z-dn.net/?f=A%20%3D%20%5Cfrac%20%7Bb%20%2A%20h%7D%20%7B2%7D)
Where:
b: It's the base
h: It's the height
We have to:
![cos (45) = \frac {b} {24}\\b = 24 * cos (45)\\b = \frac {\sqrt {2}} {2} * 24\\b = 12 \sqrt {2}](https://tex.z-dn.net/?f=cos%20%2845%29%20%3D%20%5Cfrac%20%7Bb%7D%20%7B24%7D%5C%5Cb%20%3D%2024%20%2A%20cos%20%2845%29%5C%5Cb%20%3D%20%5Cfrac%20%7B%5Csqrt%20%7B2%7D%7D%20%7B2%7D%20%2A%2024%5C%5Cb%20%3D%2012%20%5Csqrt%20%7B2%7D)
The atura will be given by:
![sin (45) = \frac {h} {24}\\h = 24 * sin (45)\\h = \frac {\sqrt {2}} {2} * 24\\h = 12 \sqrt {2}](https://tex.z-dn.net/?f=sin%20%2845%29%20%3D%20%5Cfrac%20%7Bh%7D%20%7B24%7D%5C%5Ch%20%3D%2024%20%2A%20sin%20%2845%29%5C%5Ch%20%3D%20%5Cfrac%20%7B%5Csqrt%20%7B2%7D%7D%20%7B2%7D%20%2A%2024%5C%5Ch%20%3D%2012%20%5Csqrt%20%7B2%7D)
So, the area is:
![A = \frac {12 \sqrt {2} * 12 \sqrt {2}} {2}\\A=\frac{(12\sqrt{2})^2}{2}\\A = 144](https://tex.z-dn.net/?f=A%20%3D%20%5Cfrac%20%7B12%20%5Csqrt%20%7B2%7D%20%2A%2012%20%5Csqrt%20%7B2%7D%7D%20%7B2%7D%5C%5CA%3D%5Cfrac%7B%2812%5Csqrt%7B2%7D%29%5E2%7D%7B2%7D%5C%5CA%20%3D%20144)
Answer:
144
The solution is x=3/4
How can we solve given equation?
First, we will solve like terms. Then shift constant to other side and keep x on the same side to get the value of x.
We can solve given equation as shown below:
5/2-3x-5+4x=-7/4
(5-10)/2+x=-7/4
-5/2+x=-7/4
x=5/2-7/4
x= (10-7)/4
x=3/4
Hence, the solution is x=3/4.
Learn more about Linear equations here:
brainly.com/question/43297
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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)
T=34xP
T= tip for him
P= percent he charges for tip
Answer:
im on the same question and i dont know