Answer:
2) d. 60°
3) a. AB
Step-by-step explanation:
<u>Question 2</u>
ΔABC and ΔCDA are <u>congruent</u> because:
- they are both <u>right triangles</u>
- they <u>share one side</u> (AC)
- their hypotenuse are <u>parallel</u> (marked by the arrows)
This means the corresponding side lengths and angles are equal.
Therefore,
∠CDA = ∠ABC
⇒ x = 60°
<u>Question 3</u>
The <u>hypotenuse</u> is the <u>longest side</u> of a <u>right triangle</u> - the side opposite the right angle (the right angle is shown as a small square).
Therefore, the hypotenuse of ΔABC is the line AB.
Answer:
x = 9
(5x9) - 1° = 45 - 1 or 44°
Step-by-step explanation:
the little square indicates the angle is a right angle, measuring 90°
therefore, you can solve for 'x' by creating this equation:
46 + 5x-1 = 90
45 + 5x = 90
5x = 45
x = 9
Answer:
9 ft
Step-by-step explanation:
<h3>a²+b²=c²</h3><h3>a²+12²=15²</h3><h3>a²+144=225</h3><h3>225-144=81</h3><h3>√81=9</h3>
![\textit{area of a rectangle}\\\\ A=Lw ~~ \begin{cases} L=length\\ w=width\\[-0.5em] \hrulefill\\ L=a+5\\ w=a-2\\ A=60 \end{cases}\implies 60=(a+5)(a-2) \\\\\\ 60=\stackrel{F~O~I~L}{a^2+3a-10}\implies 0=a^2+3a-70 \\\\\\ 0=(a+10)(a-7)\implies a= \begin{cases} -10\\\\ 7 ~~ \textit{\LARGE \checkmark} \end{cases}](https://tex.z-dn.net/?f=%5Ctextit%7Barea%20of%20a%20rectangle%7D%5C%5C%5C%5C%20A%3DLw%20~~%20%5Cbegin%7Bcases%7D%20L%3Dlength%5C%5C%20w%3Dwidth%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20L%3Da%2B5%5C%5C%20w%3Da-2%5C%5C%20A%3D60%20%5Cend%7Bcases%7D%5Cimplies%2060%3D%28a%2B5%29%28a-2%29%20%5C%5C%5C%5C%5C%5C%2060%3D%5Cstackrel%7BF~O~I~L%7D%7Ba%5E2%2B3a-10%7D%5Cimplies%200%3Da%5E2%2B3a-70%20%5C%5C%5C%5C%5C%5C%200%3D%28a%2B10%29%28a-7%29%5Cimplies%20a%3D%20%5Cbegin%7Bcases%7D%20-10%5C%5C%5C%5C%207%20~~%20%5Ctextit%7B%5CLARGE%20%5Ccheckmark%7D%20%5Cend%7Bcases%7D)
notice, we didn't use the negative value, valid though as it is, because in this case "a" can't be negative.
