The answers are 6i/13 and -6i/13. The work it attached below
Answer: a) Yes, there is enough fance
b) 58.1° and 47.9°
c) The city will not approve, because 1/3 of the area is just 2220.5ft²
Step-by-step explanation:
a) using law of cosines: x is the side we do not know.
x² = 126² + 110² - 2.126.110.cos74°
x² = 20335.3
x = 142.6 ft
So 150 > 142.6, there is enough fance
b) using law of sine:
sin 74/ 142.6 = sinα/126 = sinβ/110
sin 74/ 142.6 = sinα/126
0.006741 = sinα/126
sinα = 0.849
α = sin⁻¹(0.849)
α = 58.1°
sin 74/ 142.6 = sinβ/110
sin 74/ 142.6 = sinβ/110
0.006741 = sinβ/110
sinβ = 0.741
β = sin⁻¹(0.741)
β = 47.9°
Checking: 74+58.1+47.9 = 180° ok
c) Using Heron A² = p(p-a)(p-b)(p-c)
p = a+b+c/2
p=126+110+142.6/2
p=189.3
A² = 189.3(189.3-126)(189.3-110)(189.3-142.6)
A = 6661.5 ft²
1/3 A = 2220.5
So 2300 > 2220.5. The area you want to build is bigger than the area available.
The city will not approve
Answer:
A. 15
Step-by-step explanation:
To solve this you need to compare the lengths given to you in the question statement.
Because the lines originate from a single point, they're like triangles. We can easily see a triangle AGF and a triangle ADE, right?
Both triangles are similar triangles, so we can see triangle ADE as a larger version of angle AGF.
They give you the dimension of A F and A E (through A F + F E) to establish a ratio... and they give you A G, asking for A D.
So, A F = 16, A E = 20 (16 + 4), A G = 12.
Since A D is to A G what A E is to A F, we can easily make the following cross-multiplication:

So, A D = (A G * A E)/A F
A D = (12 * 20) / 16 = 15
72=1,72,2,36,3,24,4,18,6,12,8,9
28=1,28,2,14,4,7
So,the answer is 4