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3 years ago

Find sin0 where 0 is the angle shown. Give an exact value, not a decimal approximation.

Mathematics

1 answer:

otez555 [7]3 years ago

7 0

Answer: Sin0 = 8/8.5

Step-by-step explanation: What we have is a right angled triangle, with two sides given and one angle which is the reference angle (unknown angle).

The Sine of the angle is calculated as

Sin0 = opposite/hypotenuse

We have the opposite side (facing the reference angle) as 8 units and the hypotenuse (facing the right angle unknown), which we shall label as X.

To calculate the hypotenuse, we shall apply the Pythagoras theorem which is,

X² = 3² + 8²

X² = 9 + 64

X² = 73

Adding the square root sign to both sides of the equation, we now have

X = √73

X = 8.5 (approximately)

Now that we have the hypotenuse as 8.5, the Sine of the angle can now be calculated as

Sin0 = opposite/hypotenuse

Sin0 = 8/8.5

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3 years ago

What is y-intercept for the line y=8x+21

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Change Y to 0.

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3 years ago

85 is 2.5% of what number?

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3 years ago

The sum of two numbers is 47 and the difference is 25 . what are the numbers?

taurus [48]

The numbers are: 36 and 11 .
______________________________________________
Explanation:
______________________________________________
Let us represent the TWO (2) numbers with the variables;
         "x" and "y" .
__________________________________________
     x + y = 47 .

     y − x = 25.
__________________________________________
Since: " y − x = 25 " ;

Solve for "y" in terms of "x" ;

y − x = 25 ;

Add "x" to each side of the equation:
_____________________________________________
   y − x + x = 25 + x ;

to get:

   y = 25 + x .

Now, since:

x + y = 47 ;

Plug in "(25 + x)" as a substitution for "y"; to solve for "x" :

x + (25 + x) = 47 ;

x + 25 + x + 47 ;

2x + 25 = 47 ;

Subtract "25" from each side of the equation:

2x + 25 − 25 = 47 − 25 ;

2x = 22 ;

Divide EACH SIDE of the equation by "2" ;
to isolate "x" on one side of the equation; and to solve for "x" ;

2x / 2 = 22 / 2 ;

    x = 11 ;
______________________________________________
x + y = 47<span> ;

</span>Plug in "11" for "x" into the equation ; to solve for "y" ;

11 + y = 47 ;

Subtract "11" from EACH SIDE of the equation;
to isolate "y" on one side of the equation; and to solve for "y" ;

11 + y − 11 = 47 − 11 ;

            y = 36 .
___________________________________________
So: x = 11 , y = 36 ;
___________________________________________
Let us check our work:

y − x = 25 ;

36 − 11 =? 25 ? Yes!

x + y = 47 ;

36 + 11 =? 47 ? Yes!
______________________________________________
The numbers are: 36 and 11 .
______________________________________________

5 0

3 years ago

Mike traveled to Greensboro by car. Going there took 6 hours, and the return trip was four hours. Mike averaged a speed of 81 mi

Marat540 [252]

Answer: 64.8 mph

Step-by-step explanation:

Given

Arriving time is 6 hours

return time is 4 hours

The average speed of returning 81 mph

Distance traveled while returning

$\Rightarrow d=81\times 4=324\ miles$

the average speed of the entire trip is

$\Rightarrow v_{avg}=\dfrac{2\times 324}{6+4}=\dfrac{648}{10}=64.8\ mph$

4 0

3 years ago

Find sin0 where 0 is the angle shown. Give an exact value, not a decimal approximation.​

Find sin0 where 0 is the angle shown. Give an exact value, not a decimal approximation.