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3 years ago

If A=78º, b=16, c=7, what is the area of this triangle?

Mathematics

1 answer:

Andrei [34K]3 years ago

8 0

Answer:

= 54.78 square units

Step-by-step explanation:

We can calculate the area of the triangle using the formula;

Area = 1/2abSinθ ; where a and b is the sides making the angle θ.

Therefore;

Area = 1/2 bc sin C

= 1/2 × 16 × 7 × Sin 78

= 8 × 7 × sin 78

<u>= 54.78 square units</u>

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How do you Graph y-3=1/3(x+1)

jekas [21]

Answer:

You can find the point of intersection of the line with the y-axis and the the point of intersection of the line with the x-axis. See the graph attached.

Step-by-step explanation:

Find the intersection with the y-axis. Substitute $x=0$ into the equation and solve for y:

$y-3=\frac{1}{3}(x+1)\\\\y-3=\frac{1}{3}(0+1)\\\\y-3=\frac{1}{3}(1)\\y=\frac{1}{3}+3\\\\y=\frac{10}{3}$

$y$ ≈3.33

Find the intersection with the x-axis. Substitute $y=0$ into the equation and solve for x:

$y-3=\frac{1}{3}(x+1)$

$0-3=\frac{1}{3}(x+1)\\(-3)(3)=x+1\\-9-1=x\\x=-10$

Now, you know that the line passes through the point (0,3.33) and (-10,0). Now you can graph the function. (Observe the graph attached)

6 0

3 years ago

Determine whether the given vectors are orthogonal, parallel or neither. (a) u=[-3,9,6], v=[4,-12,-8,], (b) u=[1,-1,2] v=[2,-1,1

nevsk [136]

Answer:

a) $u v= (-3)*(4) + (9)*(-12)+ (6)*(-8)=-168$

Since the dot product is not equal to zero then the two vectors are not orthogonal.

$|u|= \sqrt{(-3)^2 +(9)^2 +(6)^2}=\sqrt{126}$

$|v| =\sqrt{(4)^2 +(-12)^2 +(-8)^2}=\sqrt{224}$

$cos \theta = \frac{uv}{|u| |v|}$

$\theta = cos^{-1} (\frac{uv}{|u| |v|})$

If we replace we got:

$\theta = cos^{-1} (\frac{-168}{\sqrt{126} \sqrt{224}})=cos^{-1} (-1) = \pi$

Since the angle between the two vectors is 180 degrees we can conclude that are parallel

b) $u v= (1)*(2) + (-1)*(-1)+ (2)*(1)=5$

$|u|= \sqrt{(1)^2 +(-1)^2 +(2)^2}=\sqrt{6}$

$|v| =\sqrt{(2)^2 +(-1)^2 +(1)^2}=\sqrt{6}$

$cos \theta = \frac{uv}{|u| |v|}$

$\theta = cos^{-1} (\frac{uv}{|u| |v|})$

$\theta = cos^{-1} (\frac{5}{\sqrt{6} \sqrt{6}})=cos^{-1} (\frac{5}{6}) = 33.557$

Since the angle between the two vectors is not 0 or 180 degrees we can conclude that are either.

c) $u v= (a)*(-b) + (b)*(a)+ (c)*(0)=-ab +ba +0 = -ab+ab =0$

Since the dot product is equal to zero then the two vectors are orthogonal.

Step-by-step explanation:

For each case first we need to calculate the dot product of the vectors, and after this if the dot product is not equal to 0 we can calculate the angle between the two vectors in order to see if there are parallel or not.

Part a

u=[-3,9,6], v=[4,-12,-8,]

The dot product on this case is:

$u v= (-3)*(4) + (9)*(-12)+ (6)*(-8)=-168$

Since the dot product is not equal to zero then the two vectors are not orthogonal.

Now we can calculate the magnitude of each vector like this:

$|u|= \sqrt{(-3)^2 +(9)^2 +(6)^2}=\sqrt{126}$

$|v| =\sqrt{(4)^2 +(-12)^2 +(-8)^2}=\sqrt{224}$

And finally we can calculate the angle between the vectors like this:

$cos \theta = \frac{uv}{|u| |v|}$

And the angle is given by:

$\theta = cos^{-1} (\frac{uv}{|u| |v|})$

If we replace we got:

$\theta = cos^{-1} (\frac{-168}{\sqrt{126} \sqrt{224}})=cos^{-1} (-1) = \pi$

Since the angle between the two vectors is 180 degrees we can conclude that are parallel

Part b

u=[1,-1,2] v=[2,-1,1]

The dot product on this case is:

$u v= (1)*(2) + (-1)*(-1)+ (2)*(1)=5$

Since the dot product is not equal to zero then the two vectors are not orthogonal.

Now we can calculate the magnitude of each vector like this:

$|u|= \sqrt{(1)^2 +(-1)^2 +(2)^2}=\sqrt{6}$

$|v| =\sqrt{(2)^2 +(-1)^2 +(1)^2}=\sqrt{6}$

And finally we can calculate the angle between the vectors like this:

$cos \theta = \frac{uv}{|u| |v|}$

And the angle is given by:

$\theta = cos^{-1} (\frac{uv}{|u| |v|})$

If we replace we got:

$\theta = cos^{-1} (\frac{5}{\sqrt{6} \sqrt{6}})=cos^{-1} (\frac{5}{6}) = 33.557$

Since the angle between the two vectors is not 0 or 180 degrees we can conclude that are either.

Part c

u=[a,b,c] v=[-b,a,0]

The dot product on this case is:

$u v= (a)*(-b) + (b)*(a)+ (c)*(0)=-ab +ba +0 = -ab+ab =0$

Since the dot product is equal to zero then the two vectors are orthogonal.

5 0

3 years ago

Read 2 more answers

Ⓗⓘ քɛօքlɛ

Elza [17]

The answer to this, maybe.., is 180

7 0

3 years ago

Read 2 more answers

The pool at the park is 18 feet wide how many yardsticks would it take to measure the width of the pool

sattari [20]

6 because 18 divided by 3 equals 6

4 0

3 years ago

A football team won 8 more games than they lost. They played 24 games in the season. How many games were won and how many were l

Vaselesa [24]

The team lost n games.

The team won 8 more games than it lost, so it won n + 8.

The total number of games the team played was n + n + 8, or 2n + 8.

The team played a total of 24 games, so

2n + 8 = 24

We now solve for n.

2n + 8 = 24

2n = 16

n = 8 (lost games)

n + 8 = 8 + 8 = 16 (won games)

Answer: The team won 16 games and lost 8 games.

5 0

3 years ago