Mathematics, 12.11.2019 05:31 shewag8749

Will make ! a triangular section of a lawn will be converted to river rock instead of grass. maurice insists that the only way to find a missing side length is to use the law of cosines. johanna exclaims, that only the law of sines will be useful. describe a scenario where maurice is correct, a scenario where johanna is correct, and a scenario where both laws are able to be used. use complete sentences and example measurements when necessary.

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Let's consider the triangle ABC shown in the first diagram below. We name the sides with small letters: a, b, and c. We name the angles by the capital letters A, B, and C. Side a pairs with angle A° which are opposite each other. The same with side b and angle B° and side c and angle C°.

We can use the cosine rule when we know the length of two sides and the angle opposite the side that is unknown. For example, referring to the second diagram, we know the length of side a and side b and we are looking for the length of side c. We also know the angle that is located on the opposite of side c, then to solve this we can use the cosine rule

c² = a² + b² - 2ab(cos(C°))

The third diagram shows a scenario when sine rule can be used. Say we need the length of the side c. We know the length of side a, the size of angle A° and angle C° then we can use the sine rule

$\frac{c}{sin(C)} = \frac{a}{sin(A)}$

We can also use sine rule if we know length of side b and the size of angle B° instead of side a and angle A°

Will make ! a triangular section of a lawn will be converted to river rock instead of grass. mauric

Will make ! a triangular section of a lawn will be converted to river rock instead of grass. mauric

Answer from: Quest

step-by-step explanation:

when the line is solid:

it's either < or >

when the line is dashed:

it's either < or >

this > inequality sign means:

greater thanmore thanaboveexceeds

this < inequality sign means:

less thanfewer thanbelow

this > inequality sign means:

greater than/equal tono less thanat leastminimum of

this < inequality sign means:

less than/equal tono more thanat mostmaximum of

about the problem:

since the line is solid, that means it's either < or >

srry i'm not done ! i'll

Which inequality is represented by the graph? which test point holds true for the inequality?

Answer from: Quest

a. we have two

lines: y = 4-x and

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b. 4-x = 8-x^-1

x 4-x 8-x^-1

-3 7

8.33

-2 6 8.5

-1 5 9

0 4

1 3

2 2

7.5

3 1 7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:

x=-4.236

y = 4-x = 4 – (-4.236)

= 8.236

y = 8-x^-1 = .236)^-1

= 8.236

x=0.236

y = 4-x = 4 – (0.236) = 3.764

y = 8-x^-1 = 8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c. to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x and y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines. the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!

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