This is Pythagorean theorem.
We already know a and c.
a = 4 and c = 10
4² + b² = 10²
16 + b² = 100
Subtact 16 from each side.
b² = 84
Square root of each side:
b = ≈9.165 or √84
Hope this helps!
Answer:
Step-by-step explanation:
Slope of line A = 
= 
= 3
Slope of line B = 
= 
Slope of line C = 
= 
5). Slope of the hypotenuse of the right triangle = 
= 
= 
Since slopes of line C and the hypotenuse are same, right triangle may lie on line C.
6). Slope of the hypotenuse = 
= 3
Therefore, this triangle may lie on the line A.
7). Slope of hypotenuse = 
= 
Given triangle may lie on the line C.
8). Slope of hypotenuse = 
= 
Given triangle may lie on the line B.
9). Slope of hypotenuse = 
= 
Given triangle may lie on the line B.
10). Slope of hypotenuse = 
= 3
Given triangle may lie on the line A.
Let the initial point of the vector be (x,y). Then the magnitude of the vector v can be written as:

The magnitude of vecor v is given to be 10. So we can write:

Now from the given options, we have to check which one satisfies the above equation. That point will be the initial point of the vector.
The point in option d, satisfies the equation.
Thus, the answer to this question is option D
Answer: the length of string that been let out to fly the kite this high is 172.89 ft
Step-by-step explanation:
The length of string attached to the kite, the vertical height of the kite above the ground and the ground distance forms a right angle triangle.
With an angle of 57 degrees, the length of the string that is attached to the kite represents the hypotenuse of the right angle triangle.
The height of the kite above the ground represents the opposite side of the triangle
To determine h, the length of the string that has been let out to fly the kite this high, we would apply the
Sine trigonometric ratio which is expressed as
Sine θ = opposite side/hypotenuse
Sin 57 = 145/h
h = 145/Sin57 = 145/0.8387
h = 172.89
Answer:
23. 0.4583 seconds
24. 0.0107 seconds
Step-by-step explanation:
The problem statement tells you how to work it. You need to convert speed from miles per hour to feet (or inches) per second.
90 mi/h = (90·5280 ft)/(3600 s) = 132 ft/s = (132·12 in)/s = 1584 in/s
__
23. The time it takes for the ball to travel 60.5 ft is ...
time = distance/speed
time = (60.5 ft)/(132 ft/s) = 0.4583 s
It takes 458.3 milliseconds to reach home plate.
__
24. time = distance/speed
time = (17 in)/(1584 in/s) = 0.0107 s
The ball is in the strike zone for 10.7 milliseconds.