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
42.5 units sq
I’m not sure because I did this partly in my head but this should be right.
<h2>
Answers:</h2>
- Solving for x on the question - <em>2x + 3y = 32</em> |
- Answer : x =
⁻y + 16
- Solving for y on the question - <em>2x + 3y = 32</em> |
- Answer : y =
x +
<h3>
</h3>
- Solving for x on question - 5x - 4y = -81 |
- Answer : x =
y + 
- Solving for y on question - 5x - 4y = -81 |
- Answer : y =
x + 
<h2>
Step-by-step explanation:</h2>
<em>(Solving for x on question - 2x + 3y = 32)</em>
2x + 3y = 32
Step 1: Add -3y to both sides.
2x + 3y + −3y = 32 + −3y
2x = −3y + 32
Step 2: Divide both sides by 2.
= 
<u>x = </u>
<u>⁻y + 16</u><u> </u>
<em>(Solving for y on question - 2x + 3y = 32)</em>
2x + 3y = 32
Step 1: Add -2x to both sides.
2x + 3y + −2x = 32+ −2x
3y = −2x + 32
Step 2: Divide both sides by 3.
= 
<u>y = </u>
<u>x + </u>
<u> </u>
<em>(Solving for x on question - 5x - 4y = -81)</em>
5x − 4y = −81
Step 1: Add 4y to both sides.
5x − 4y + 4y = −81 + 4y
5x = 4y − 81
Step 2: Divide both sides by 5.
=
<u>x = </u>
<u>y + </u>
<u> </u>
<em>(Solving for y on question - 5x - 4y = -81 )</em>
5x − 4y = −81
Step 1: Add -5x to both sides.
5x − 4y + −5x = −81 + −5x
−4y = −5x − 81
Step 2: Divide both sides by -4.
=
y =
x + 
Answer:
The answer is 55.54778 ft^2
Step-by-step explanation:
below in the picture.
Y - y₁ = m (x-x₁)
y - (-5) = 0 (x-2)
y + 5 = 0
y = -5