Specific data is show I believe
You can find the area of Bonnue's backyard by comparing the hypotenuse of the garden to the hypotenuse of the back yard. If the hypotenuse of the garden is 10 (with the side lengths being 6, 8 and 10 - the longest is always the hypotenuse) and the hypotenuse of the back yard is 30, this is a scale factor of 3 (3 times longer).
This means the other two sides would also be 3 times longer.
6 yards x 3 = 18
8 yards x 3 = 24
To find the area using these dimensions, you will use the formula for finding the area of a triangle.
A = 1/2bh
A = 1/2 x 18 x 24
A = 216 square yards
The area of the backyard is 216 square yards.
Answer:
![z=\frac{15\sqrt{3}}{2}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B15%5Csqrt%7B3%7D%7D%7B2%7D)
Step-by-step explanation:
In leftmost triangle:
opposite side =y
adjacent=a
now, we can use trig formula
![tan(60)=\frac{y}{a}](https://tex.z-dn.net/?f=tan%2860%29%3D%5Cfrac%7By%7D%7Ba%7D)
now, we can solve for y
![y=atan(60)](https://tex.z-dn.net/?f=y%3Datan%2860%29)
In rightmost triangle:
adjacent=b
opposite=y
a+b=15
b=15-a
now, we can use trig formula
![tan(30)=\frac{y}{15-a}](https://tex.z-dn.net/?f=tan%2830%29%3D%5Cfrac%7By%7D%7B15-a%7D)
now, we can solve for y
![y=(15-a)tan(30)](https://tex.z-dn.net/?f=y%3D%2815-a%29tan%2830%29)
now, we can set them equal
and then we can solve for a
![atan(60)=(15-a)tan(30)](https://tex.z-dn.net/?f=atan%2860%29%3D%2815-a%29tan%2830%29)
![\sqrt{3}a\cdot \:3=\frac{\sqrt{3}\left(15-a\right)}{3}\cdot \:3](https://tex.z-dn.net/?f=%5Csqrt%7B3%7Da%5Ccdot%20%5C%3A3%3D%5Cfrac%7B%5Csqrt%7B3%7D%5Cleft%2815-a%5Cright%29%7D%7B3%7D%5Ccdot%20%5C%3A3)
![4\sqrt{3}a=15\sqrt{3}](https://tex.z-dn.net/?f=4%5Csqrt%7B3%7Da%3D15%5Csqrt%7B3%7D)
![a=\frac{15}{4}](https://tex.z-dn.net/?f=a%3D%5Cfrac%7B15%7D%7B4%7D)
now, we can find b
![b=15-\frac{15}{4}](https://tex.z-dn.net/?f=b%3D15-%5Cfrac%7B15%7D%7B4%7D)
![b=\frac{45}{4}](https://tex.z-dn.net/?f=b%3D%5Cfrac%7B45%7D%7B4%7D)
now, we can use trig formula
![cos(30)=\frac{b}{z}](https://tex.z-dn.net/?f=cos%2830%29%3D%5Cfrac%7Bb%7D%7Bz%7D)
now, we can find z
![z=\frac{\frac{45}{4}}{cos(30)}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B%5Cfrac%7B45%7D%7B4%7D%7D%7Bcos%2830%29%7D)
we can simplify it
and we get
![z=\frac{15\sqrt{3}}{2}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B15%5Csqrt%7B3%7D%7D%7B2%7D)
Minust 5x both sides
7x-5x<5x-5x-8
2x<-8
divide by 2 both sides
x<-4