The angle diagonal to 103° is equal to 103°. So here's your equation:
(103+14x+7)°=180°
So now you can simplify:
110°+14x=180°
now subtract 110 on both sides
14x=70°
now divide by 14 on both sides
so the answer is x=5°
hope this helps
0, 1/2, -53, and 0.433 all belong in rational category
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
1∪ 2/3.....................
The answer is 93. The angle looks really close to 90 and 93 is the closest.
