The angle should be 24 degrees
Answer:
i think its c
sorry if im wrong!
Step-by-step explanation:
The answer is communicative
Answer:
The vertical angles are ∠ WRS and ∠ VRT ⇒ 2nd answer
Step-by-step explanation:
right on edge 2020
Answer:
7 feet and 24 feet
Step-by-step explanation:
In the right triangle, the hypotenuse is 25 feet long. The area of this triangle is 84 square feet.
Let x feet and y feet be the lengths of triangle's legs.
By the Pythagorean theorem,
![x^2+y^2=25^2\\ \\x^2+y^2=625](https://tex.z-dn.net/?f=x%5E2%2By%5E2%3D25%5E2%5C%5C%20%5C%5Cx%5E2%2By%5E2%3D625)
The area of the right triangle is half the product of its legs, thus
![84=\dfrac{1}{2}xy\\ \\xy=168](https://tex.z-dn.net/?f=84%3D%5Cdfrac%7B1%7D%7B2%7Dxy%5C%5C%20%5C%5Cxy%3D168)
Solve the system of two equations:
![\left\{\begin{array}{l}x^2+y^2=625\\ \\xy=168\end{array}\right.](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bl%7Dx%5E2%2By%5E2%3D625%5C%5C%20%5C%5Cxy%3D168%5Cend%7Barray%7D%5Cright.)
From the second equation:
![x=\dfrac{168}{y}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B168%7D%7By%7D)
Substitute it into the first equation:
![\left(\dfrac{168}{y}\right)^2+y^2=625\\ \\168^2+y^4=625y^2\\ \\y^4-625y^2+168^2=0\\ \\D=(-625)^2-4\cdot 168^2=(625-2\cdot 168)(625+2\cdot 168)=289\cdot 961=17^2\cdot 31\\ \\\sqrt{D}=17\cdot 31=527\\ \\y^2_{1,2}=\dfrac{-(-625)\pm 527}{2}=49,\ 576\\ \\y_1=7,\ y_2=-7,\ y_3=24,\ y_4=-24](https://tex.z-dn.net/?f=%5Cleft%28%5Cdfrac%7B168%7D%7By%7D%5Cright%29%5E2%2By%5E2%3D625%5C%5C%20%5C%5C168%5E2%2By%5E4%3D625y%5E2%5C%5C%20%5C%5Cy%5E4-625y%5E2%2B168%5E2%3D0%5C%5C%20%5C%5CD%3D%28-625%29%5E2-4%5Ccdot%20168%5E2%3D%28625-2%5Ccdot%20168%29%28625%2B2%5Ccdot%20168%29%3D289%5Ccdot%20961%3D17%5E2%5Ccdot%2031%5C%5C%20%5C%5C%5Csqrt%7BD%7D%3D17%5Ccdot%2031%3D527%5C%5C%20%5C%5Cy%5E2_%7B1%2C2%7D%3D%5Cdfrac%7B-%28-625%29%5Cpm%20527%7D%7B2%7D%3D49%2C%5C%20576%5C%5C%20%5C%5Cy_1%3D7%2C%5C%20y_2%3D-7%2C%5C%20y_3%3D24%2C%5C%20y_4%3D-24)
The length of the leg cannot be negative, so
![y_1=7\Rightarrow x_1=\dfrac{168}{7}=24\\ \\y_2=24\Rightarrow x_2=\dfrac{168}{24}=7](https://tex.z-dn.net/?f=y_1%3D7%5CRightarrow%20x_1%3D%5Cdfrac%7B168%7D%7B7%7D%3D24%5C%5C%20%5C%5Cy_2%3D24%5CRightarrow%20x_2%3D%5Cdfrac%7B168%7D%7B24%7D%3D7)