Answer:
212
Step-by-step explanation:
13 * 17 = 221
221- 9 = 212
Step-by-step explanation:
Use the Pythagorean theorem:
![leg^2+leg^2=hypotenuse^2](https://tex.z-dn.net/?f=leg%5E2%2Bleg%5E2%3Dhypotenuse%5E2)
We have
![leg=4,\ hypotenuse=10](https://tex.z-dn.net/?f=leg%3D4%2C%5C%20hypotenuse%3D10)
Substitute:
![4^2+leg^2=10^2](https://tex.z-dn.net/?f=4%5E2%2Bleg%5E2%3D10%5E2)
<em>subtract 16 from both sides</em>
![leg^2=84\to leg=\sqrt{84}\\\\leg=\sqrt{(4)(21)}\\\\leg=\sqrt4\cdot\sqrt{21}\\\\leg=2\sqrt{21}](https://tex.z-dn.net/?f=leg%5E2%3D84%5Cto%20leg%3D%5Csqrt%7B84%7D%5C%5C%5C%5Cleg%3D%5Csqrt%7B%284%29%2821%29%7D%5C%5C%5C%5Cleg%3D%5Csqrt4%5Ccdot%5Csqrt%7B21%7D%5C%5C%5C%5Cleg%3D2%5Csqrt%7B21%7D)
![sine=\dfrac{opposite}{hypotenuse}\\\\cosine=\dfrac{adjacent}{hypotenuse}\\\\tangent=\dfrac{opposite}{adjacent}\\\\cotangent=\dfrac{adjacent}{opposite}\\\\secant=\dfrac{hypotenuse}{adjacent}\\\\cosecant=\dfrac{hypotenuse}{opposite}](https://tex.z-dn.net/?f=sine%3D%5Cdfrac%7Bopposite%7D%7Bhypotenuse%7D%5C%5C%5C%5Ccosine%3D%5Cdfrac%7Badjacent%7D%7Bhypotenuse%7D%5C%5C%5C%5Ctangent%3D%5Cdfrac%7Bopposite%7D%7Badjacent%7D%5C%5C%5C%5Ccotangent%3D%5Cdfrac%7Badjacent%7D%7Bopposite%7D%5C%5C%5C%5Csecant%3D%5Cdfrac%7Bhypotenuse%7D%7Badjacent%7D%5C%5C%5C%5Ccosecant%3D%5Cdfrac%7Bhypotenuse%7D%7Bopposite%7D)
Substitute:
![hypotenuse=10,\ opposite=4,\ adjacent=2\sqrt{21}](https://tex.z-dn.net/?f=hypotenuse%3D10%2C%5C%20opposite%3D4%2C%5C%20adjacent%3D2%5Csqrt%7B21%7D)
![\sin\theta=\dfrac{4}{10}=\dfrac{2}{5}\\\\\cos\theta=\dfrac{2\sqrt{21}}{10}=\dfrac{\sqrt{21}}{5}\\\\\tan\theta=\dfrac{4}{2\sqrt{21}}=\dfrac{2}{\sqrt{21}}\cdot\dfrac{\sqrt{21}}{\sqrt{21}}=\dfrac{2\sqrt{21}}{21}\\\\\cot\theta=\dfrac{2\sqrt{21}}{4}=\dfrac{\sqrt{21}}{2}\\\\\sec\theta=\dfrac{10}{2\sqrt{21}}=\dfrac{5}{\sqrt{21}}\cdot\dfrac{\sqrt{21}}{\sqrt{21}}=\dfrac{5\sqrt{21}}{21}\\\\\csc\theta=\dfrac{10}{4}=\dfrac{5}{2}](https://tex.z-dn.net/?f=%5Csin%5Ctheta%3D%5Cdfrac%7B4%7D%7B10%7D%3D%5Cdfrac%7B2%7D%7B5%7D%5C%5C%5C%5C%5Ccos%5Ctheta%3D%5Cdfrac%7B2%5Csqrt%7B21%7D%7D%7B10%7D%3D%5Cdfrac%7B%5Csqrt%7B21%7D%7D%7B5%7D%5C%5C%5C%5C%5Ctan%5Ctheta%3D%5Cdfrac%7B4%7D%7B2%5Csqrt%7B21%7D%7D%3D%5Cdfrac%7B2%7D%7B%5Csqrt%7B21%7D%7D%5Ccdot%5Cdfrac%7B%5Csqrt%7B21%7D%7D%7B%5Csqrt%7B21%7D%7D%3D%5Cdfrac%7B2%5Csqrt%7B21%7D%7D%7B21%7D%5C%5C%5C%5C%5Ccot%5Ctheta%3D%5Cdfrac%7B2%5Csqrt%7B21%7D%7D%7B4%7D%3D%5Cdfrac%7B%5Csqrt%7B21%7D%7D%7B2%7D%5C%5C%5C%5C%5Csec%5Ctheta%3D%5Cdfrac%7B10%7D%7B2%5Csqrt%7B21%7D%7D%3D%5Cdfrac%7B5%7D%7B%5Csqrt%7B21%7D%7D%5Ccdot%5Cdfrac%7B%5Csqrt%7B21%7D%7D%7B%5Csqrt%7B21%7D%7D%3D%5Cdfrac%7B5%5Csqrt%7B21%7D%7D%7B21%7D%5C%5C%5C%5C%5Ccsc%5Ctheta%3D%5Cdfrac%7B10%7D%7B4%7D%3D%5Cdfrac%7B5%7D%7B2%7D)
Answer:
1
Step-by-step explanation:
0
=
9
3
<h3>
Answer: A) 5 units</h3>
====================================================
Explanation:
The two points given are
C = (x1,y1) = (2,-1)
D = (x2,y2) = (5,3)
Use the distance formula
![d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(2-5)^2 + (-1-3)^2}\\\\d = \sqrt{(-3)^2 + (-4)^2}\\\\d = \sqrt{9 + 16}\\\\d = \sqrt{25}\\\\d = 5\\\\](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%28x_1%20-%20x_2%29%5E2%20%2B%20%28y_1%20-%20y_2%29%5E2%7D%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B%282-5%29%5E2%20%2B%20%28-1-3%29%5E2%7D%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B%28-3%29%5E2%20%2B%20%28-4%29%5E2%7D%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B9%20%2B%2016%7D%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B25%7D%5C%5C%5C%5Cd%20%3D%205%5C%5C%5C%5C)
The distance from C to D is 5 units. This is the same as saying segment CD is 5 units long.