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mrs_skeptik [129]
3 years ago
12

The perimeter of an equilateral triangle is 27 centimeters. Find the altitude of the triangle

Mathematics
1 answer:
Alinara [238K]3 years ago
6 0
9^2 = 4.5^2+b^2
81=20.25+b^2
60.75=b^2
b (altitude) = approx. 7.8
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Two streets bounding your triangular lot make an angle of 74∘. The lengths of the two sides of the lot on these streets are 126
ycow [4]

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)

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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

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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

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Answer:

Step-by-step explanation:

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Answer:

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