1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Lelu [443]
1 year ago
10

The cheetah area at a zoo is designed in a triangular fashion, surrounded on all three sides by sidewalks. The property has 67 f

eet of frontage on one sidewalk, and 48 feet of frontage on another; these two sidewalks intersect at a 72° angle. What is the square footage of the cheetahs' habitat? Round to the nearest hundredth.
Mathematics
1 answer:
Strike441 [17]1 year ago
7 0

1529.3 square unit is the area of the cheetah area at a zoo is designed in a triangular fashion, surrounded on all three sides by sidewalks, given that the property has 67 feet of frontage on one sidewalk, and 48 feet of frontage on another; these two sidewalks intersect at a 72° angle. This can obtained by using the formula of Area of a Triangle with 2 Sides and Included Angle.

<h3>Find the area of the cheetah area at the zoo:</h3>

Area of a triangle is obtained using the formula of Area of a Triangle with 2 Sides and Included Angle.

If in a triangle ΔABC,

  • 1/2 × bc × sin(A), if b and c are two sides of a triangle and angle A is the included angle
  • 1/2 × ac × sin(B), if a and c are two sides of a triangle and angle B is the included angle
  • 1/2 × ab × sin(C), if a and b are two sides of a triangle and angle C is the included angle

Here it is given that,

67 feet and 48 feet are the sides of the triangular space and angle 72° is the included angle.

By using the formula of Area of a Triangle with 2 Sides and Included Angle,

Area of the cheetah area = 1/2 × bc × sin(A)

Area of the cheetah area = 1/2 × (67)(48) × sin(72°)

sin(72°) = 0.951056516

Area of the cheetah area = 1608 × 0.951056516

Area of the cheetah area = 1529.29888 ≈ 1529.3 square unit

             

Hence 1529.3 square unit is the area of the cheetah area at a zoo is designed in a triangular fashion, surrounded on all three sides by sidewalks, given that the property has 67 feet of frontage on one sidewalk, and 48 feet of frontage on another; these two sidewalks intersect at a 72° angle.

   

Learn more about area of triangle here:

brainly.com/question/19305981

#SPJ1

You might be interested in
Help i need it asap 50 piontss and brailiest
yuradex [85]

Answer:

  1. b
  2. f
  3. e
  4. c
  5. h
  6. d
  7. g
  8. a

Step-by-step explanation:

< or > will give you an open dot which means it is not filled in.

≤ or ≥ will give you a closed dot which means it is filled in.

So for example number one:

x > 0 translated is x is greater than zero.

So look on the number line for an open dot on zero going toward the left (the side where the numbers get smaller). The rest are self explanatory.

8 0
3 years ago
What is the exact value of tan 30° ? Enter your answer, as a simplified fraction, in the box.
Romashka [77]
Hmmm if you don't have a Unit Circle, this is a good time to get one, many you can find online.  Anyhow, check your unit circle for cos(30°) and sin(30°).

\bf tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)}\qquad \qquad tan(30^o)=\cfrac{sin(30^o)}{cos(30^o)}&#10;\\\\\\&#10;tan(30^o)=\cfrac{\quad \frac{1}{2}\quad }{\frac{\sqrt{3}}{2}}\implies tan(30^o)=\cfrac{1}{2}\cdot \cfrac{2}{\sqrt{3}}\implies tan(30^o)=\cfrac{1}{\sqrt{3}}&#10;\\\\\\&#10;\stackrel{\textit{and now if we rationalize the denominator}}{\cfrac{1}{\sqrt{3}}\cdot \cfrac{\sqrt{3}}{\sqrt{3}}\implies \cfrac{\sqrt{3}}{(\sqrt{3})^2}\implies \cfrac{\sqrt{3}}{3}}
8 0
3 years ago
Read 2 more answers
Simplify the expression 6 + 3(2x - 4(3x - 2)].​
I am Lyosha [343]

Answer:

-30x + 30

Step-by-step explanation:

6 + 3 × [2x - 12x + 8]

6 + (-30x) + 24

-30x + 24

hope its correct if not sorry

8 0
3 years ago
What is the distance to the earth’s horizon from point P?<br><br> Express your answer as a decimal
rewona [7]

Answer:

The distance to the earth's horizon from point P is 216.2198187 mi, appriximately 216.22 mi

Step-by-step explanation:

This is a right triangle:

Hypotenuse: c=3959 mi + 5.9 mi → c=3964.9 mi

Leg 1: a=x=?

Leg 2: b=3959 mi

Using the Pytagorean theorem:

a^2+b^2=c^2

Replacing the known values:

(x)^2+(3959 mi)^2=(3964.9 mi)^2

Solving for x: Squaring:

x^2+15,673,681 mi^2=15,720,432.01 mi^2

Subtracting 15,673,681 mi^2 both sides of the equation:

x^2+15,673,681 mi^2-15,673,681 mi^2=15,720,432.01 mi^2-15,673,681 mi^2

x^2=46,751.01 mi^2

Square root both sides of the equation:

sqrt(x^2)=sqrt(46,751.01 mi^2)

x=216.2198187 mi

x=216.22 mi

3 0
3 years ago
A bus is carrying 60 passengers. This is 5/6 of the capacity of the bus. What is the capacity of the bus?
igor_vitrenko [27]

Answer:

72

Step-by-step explanation:

I did the math

please mark brainliest

6 0
2 years ago
Read 2 more answers
Other questions:
  • NEED HELP ASAP!!!! 40PTS IM DESPRATE
    15·2 answers
  • How many significant figures are in the measurement 20,500 liters?
    13·1 answer
  • Can u solve these for me I need help show work pls
    7·2 answers
  • A circle has a diameter with endpoints at (10,8) and (5,-4) what is the circumference of the circle
    13·1 answer
  • Which table represents the graph of a logarithmic function in the form y-log, when : &gt; 1?
    10·1 answer
  • Laura orders 50 m² of concrete paving slabs. The slabs cost £16.75 per m². How much do the slabs cost in total
    9·1 answer
  • You drink 2/7 of a pitcher of lemonade. Your friend drinks 3/14 of the pitcher. What fraction of the pitcher do you and your fri
    6·1 answer
  • He measured the pool’s dimensions to be 15 feet long by 35 feet wide. The actual dimensions of the pool are 14.5 feet by 34.75 f
    12·1 answer
  • 20 POINTS PLS HELP<br> (((95*26)-470)/16)-35=______________<br> not 4 a test
    10·2 answers
  • HELP IM ON A TIMED QUIZ
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!