Mark rides his bike from his house to the closest edge of the park, across the length of the park, and then back home. The distance from his house to the closest edge of the park is 0.9 km and the distance from the far side of the park to his house is 1.6 km. The map shows the path Mark took on his bike. If ∠B = 85° on the map, then use the law of cosines to determine the length of the park in kilometers.

Answers

Answer 1

Answer:

The length of the park is approximately 1.77 kilometers

Step-by-step explanation:

The law of cosines is most appropriate when the measures of two sides and the included angle formed n=by the path of motion is known

The given parameters of the question are;

The distance from Mark's house to the edge of the park, a = 0.9 km

The distance from the far side of the park to Mark's house, c = 1.6 km

Whereby the included angle between lines, 'a' and 'c' is the ∠B = 85°, by cosine rule, we have;

b² = a² + c² - 2·a·c·cos(B)

Where;

b = The length of the park in kilometers

By plugging in the known values of 'a', 'b', and 'c', we get;

b² = 0.9² + 1.6² - 2 × 0.9 × 1.6 × cos(85°) ≈ 3.11899146089

∴ b = √(3.11899146089) ≈ 1.76606666377

Therefore, the length of the park, b ≈ 1.77 km.


Related Questions

Any ways i need help (16 points)

Answers

Answer:

Step-by-step explanation:

A = 3M

J = 2A

J = 6M

Marie = M

Andre = 3M

Jane = 6M

6M+3M+M = 840

10M = 840

M= 84 Pounds

Andre = 3M

Andre = 84*3

Andre has 252 pounds of apples.

30 POINTSSSS ANSWER CORRECTLY THE LAST GUY TROLLED :/

Answers

Answer:

1.

A: Rectangular prism

B: Square pyramid

C: Triangular prism

2.

A: 82 square units

B: 48 square units

C: 48 square units (again)

Somehow Nets B & C have the same surface area.

Step-by-step explanation:

2A:

2(6 * 5) + 2(5) + 2(6)

2(30) + 10 + 12

60 + 22

82 square units

2B:

4((4 * 4)/2) + (4 * 4)

4(16/2) + 16

4(8) + 16

32 + 16

48 square units

2C:

2((3 * 4)/2) + (3 * 3) + (3 * 4) + (3 * 5)

2(12/2) + 9 + 12 + 15

12 + 9 + 27

12 + 36

48 square units

The area of the rectangle below is 18 square units. What is the width of the rectangle? Write and solve a division equation to find the width of the rectangle.

Answers

Answer:

24/5 or 4 and 4/5

Step-by-step explanation:

3 and 3/4=15/4

18 divided by 15/4=4 and 4/5

4 and 4/5=24/5

24/5 times 15/4=18

Answer:

I agree with the person above but I'm not so sure.

Cole wrote the number shown.

375,819

Lindsay used the same digits to write a number in which the value of the digit 7 is 110 of the value of the digit 7 in Cole’s number. Which number can be the one Lindsay wrote

Answers

the answer is the experience

Ryan invests $8,361 in a savings account with a fixed annual interest rate of 4.31% compounded monthly. After 10 years, what will be the balance in the account?

Answers

Answer:

12,750

Step-by-step explanation:

After investing for 10 years at 4.31% interest, your $8,361 investment will have grown to $12,750

Type a digit that makes this sentence true !!!

Answers

Answer:

any number between 83 and 0. [tex]0\leq x\leq 83[/tex]

Step-by-step explanation:

the number 1,548.4484 has the last two digits of 84.

And since the number has to be less than the other number and you can only switch the last two digits in the decimal's place. It has to be less than 84

Hope that helps :)

Answer:

the digit is 4, because that has 4484 but just put 4444

hey can you help me fast!!

Answers

Answer:

-10 / -2/5

Step-by-step explanation:

-10 / -2/5 = 25

25 is greater than 10

i have no idea what to do, someone pleasehelp.. please just give the straight forward equation and answer. thank you, 33 points to whoever does it

Answers

Answer:

Coordinates (1,6)

Equation x=1

Step-by-step explanation:

Center of highest point is 1 on the x and 6 on the y

Can y’all help with geo?

Answers

Here's the solution,

figure 1.

by using trigonometry,

=》

[tex] \sin(60) = \dfrac{5 \sqrt{3} }{y} [/tex]

=》

[tex] \dfrac{ \sqrt{3} }{2} = \dfrac{5 \sqrt{3} }{y} [/tex]

=》

[tex] \dfrac{1}{y} = \dfrac{ \sqrt{3} }{2 \times 5 \sqrt{3} } [/tex]

=》

[tex] \dfrac{1}{y} = \dfrac{1}{10} [/tex]

=》

[tex]y = 10[/tex]

And,

=》

[tex] \cos(60) = \dfrac{w}{y} [/tex]

=》

[tex] \dfrac{1}{2} = \dfrac{w}{10} [/tex]

=》

[tex]w = 5[/tex]

So, values are :

y = 10w = 5

figure 2.

Since, it's an isosceles triangle, w = y,

So, by pythagoras theorem :

=》

[tex] {w}^{2} + {y}^{2} = (7 \sqrt{2} ) {}^{2} [/tex]

=》

[tex] {w}^{2} + {w}^{2} = 98[/tex]

=》

[tex]2 {w}^{2} = 98[/tex]

=》

[tex] {w}^{2} = 49[/tex]

=》

[tex]w = \sqrt{49} [/tex]

=》

[tex]w = 7[/tex]

and we know, w = y, so their values will be equal to 7 units.

How much of 27 and 19 do I need to make 30,000 even?​

Answers

Answer:

I don’t know but I know 27 times 630 plus 19 times 680 is 29,930 I’ve tried some other ways but it gets really close but not exact

Step-by-step explanation:

Please help; I'll give brainliest for the first person who answers <3

Answers

Answer:

m puq

Step-by-step explanation:

Find the value of x. Round to the nearest tenth.

Answers

Answer:

90 hope this helps

Step-by-step explanation:

Hal put $3000 into a savings account that earns 6% interest. After 6 years, what will be the total amount of money in his savings account?

Explain for BRAINLIST.

Answers

Answer:

6000

Step-by-step explanation:

so you have to divide 3000 and 6 to get 500

next you would do  500 times 6 equals = 3000

so now you would plus them and get 6000

now that is your answer

please give me branlyiest

Solve the equation: 5.4 -7.5 -6.3 = Solve the equation:​

Answers

The answer would be -8.4.

Answer:

[tex]5.4 - 7.5 - 6.3 = 5.4 - 13.8 \\ = - 8.4[/tex]

Mr. Davis is packing a box with books. The box is a rectangular prism with the 2 ft 3 ft 2 ft What is the volume of the box?

Answers

Answer:

12 ft^3

Step-by-step explanation:

Given data

Dimension

Lenght= 2ft

Width= 3ft

Height= 2ft

The expression for the volume is

Volume= L*W*H

Substitute

V= 2*3*2

V= 12 ft^3

Hence the volume of the box is 12 ft^3

Find the slope of the line through each pair of points using the formula.
(17, -19) (4, -15)

Answers

Answer:

-4/13

Step-by-step explanation:

(17 , -19)  ; (4 , -15)

Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

          [tex]= \frac{-15-[-19]}{4-17}\\\\=\frac{-15+19}{4-17}\\\\=\frac{4}{-13}\\\\= \frac{-4}{13}[/tex]

Answer:

- 4 / 13

Step-by-step explanation:

Algebra work is easy :)

good luckkk

Which category best describes the group of shapes

Answers

Answer:

Parallelograms

Step-by-step explanation:

Help please I’ll give brainliest

Answers

X=20 because 28/7 is 4 and 5*4 is 20
x=20 bc 7x4=28 therefor 5x4=20

what power do I need to raise both sides of the following equation to? x^4=81

Answers

Answer:

Rise it to 2

( x ^2 ) ^2 − 9 ^2 = 0

Step-by-step explanation:

Find x and y
Show all the work

Answers

Answer:

x=27°

y=4 units

Step-by-step explanation:

To find x:

The sum of all the angles in a quadrilateral is 360°. In a rhombus (you know it's a rhombus because it's a quatrilateral where all the sides are congruent), opposite angles are congruent. Because you're given that the measure of ∠T is 127°, you also know that m∠V=127°. You also know that m∠U=m∠S=(2x-1)°.

Using this information, set up an equation.

127+127+(2x-1)+(2x-1)=360

You can just divide both sides by 2 to get:

127+(2x-1)=180

Then, just solve for x.

127+2x-1=180

2x+126=180

2x=54

x=27°

To find y:

All the sides are given to be congruent. That's what the little marks on the sides mean, and that's how we knew it was a rhombus earlier.

So SV=VU=UT=TS

SV=6y-5

VU=3y+7

Since SV=VU:

6y-5=3y+7

Solve for y.

3y=12

y=4

Hope I could help!

Please help.
Is algebra.

Answers

Answer:

B

Step-by-step explanation:

The first one is a binomial. It has two different terms on either side of the middle minus sign. y is raised to the 4 th power so that is degree 4. The answer is b

The second problem is ordered as 4 3 1 2

The powers determine the degree. The terms are all different and the number of terms is determined by the powers of the letters in the terms.

Answer:

Step-by-step explanation:

(9 x 10^6) + (8 x 10^{-4})

Answers

i think it would be 9000000.0008

A group of students is trying to determine the number of cars that move along a certain section of roadway. The dot plot below shows the speeds of 20 vehicles. Complete the table with the correct values from the dot plot.

Answers

Answer:# of cars: 1 | 0 | 0 | 0 | 2 | 4 | 5 | 3 | 0 | 2 | 2 | 1 |

Note: the answers are from left to right in order

Step-by-step explanation:

So this isn't as hard as it seems. You just count the X's and if there is like for example 1 x on 30 then the answer for 30 is 1 since there is only 1 X.

If p=9 and q=30, evaluate the following expression:p−q/3​

Answers

Answer:

-1

Step-by-step explanation:

p = 9

q = 30

p - q/3

9 - 30/3

9 - 10

-1

Make a table of values given that “x” is an integer such that -4 < x < 4, using the Equation y = 3x + 5.

Answers

I think the answer is x=6

Sam paid $8.28 for 18 stamps. At this rate, how much would it cost Sam to buy 12 stamps?

Answers

Answer: $5.52

Step-by-step explanation:

Given: Sam paid $8.28 for 18 stamps.

Thus, the cost of 18 stamps = $8.28

Then the cost of 1 stamp=

Thus, the cost of 1 stamp=$0.46

With the same rate , the cost of 12 stamps=

Therefore, the cost of 12 stamps= $5.52

hence, it costs $5.52 to Sam to buy 12 stamps.

8.28÷18 = 0.46

0.46 is the cost if 1 stamp

cost of 12 stamps= 0.46×12 = $5.52

happy to help :)

What is the asymptote of this function?

A) x=3
B) y=3
C) x=4
D) y=4

Answers

Answer:

b

Step-by-step explanation

look at the way the way the line curves and cross over into the positive across the dotted line. the curw = y

The correct answer is B

Find the trigonometric ratios as simplified fractions and as decimals to the nearest thousandths (as necessary).



Sin X: Fraction_______ Decimal_______

Cos X: Fraction_______ Decimal______

Tan X: Fraction__________ Decimal______

Answers

Step-by-step explanation:

by using Pythagoras law

ZY=√{45²-27²)=36

sin X=ZY/XY=36/45=0.8

Cos X=XZ/XY=27/45=0.6

Tan X= YZ/XZ=36/27=1.33

Angle X and Angle Y are complementary angles. Given Angle Y is equal to 1/5th Angle X. Find the value of Angle X in degrees

Answers

Answer:

75 degrees

Step-by-step explanation:

Complementary angles equal 90 degrees together. That is the case with angle X and Y. Set an equation to describe the situation.

Y=1/5X

X=5Y

Now, set another equation:

X+Y=90

Substitute the first equation into the second one.

5Y+Y=90

6Y=90

Y=15

Substitute this once again:

X+15=90

X=75

Jack invested $2,900 in an account paying an interest rate of 8 % compounded
annually. Anthony invested $2,900 in an account paying an interest rate of 82%
compounded continuously. After 10 years, how much more money would Anthony
have in his account than Jack, to the nearest dollar?

Answers

Answer: $628

Step-by-step explanation:

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