Respuesta :
Answer:
1. Option A
2. Option B
3. Option D
4. Option C
Step-by-step explanation:
The given vertices of triangle ABC are A(-3, 6), B(2,1), C(9, 5).
We have to fine the distance AB, BC and AC.
To calculate the distance between two vertices we will use the formula
[tex]d=\sqrt{(x-x')^{2}+(y-y')^{2}}[/tex]
For the length of side AB
AB=[tex]\sqrt{(2+3)^{2}+(1-6)^{2}}=\sqrt{5^{2}+5^{2}}=\sqrt{50}[/tex]
Option A. is the correct option
For the length of side BC
[tex]BC=\sqrt{(9-2)^{2}+(5-1)^{2}}=\sqrt{7^{2}+4^{2}}=\sqrt{65}[/tex]
Option B is the answer.
For the length of side AC
[tex]AC=\sqrt{(9+3)^{2}+(5-6)^{2}}=\sqrt{12^{2}+(-1)^{2}}=\sqrt{145}[/tex]
Option D is the answer.
For ∠ABC we will use the formula [tex]tan\theta =\frac{m_{1}-m_{2}}{1+m_{1}m_{2}}[/tex]
Since angle ABC is formed by two sides AB and BC
So we will find the slopes of these two lines and find the angle
Now slope of AB, [tex]m_{1}=\frac{y-y'}{x-x'}=\frac{1-6}{2+3}=\frac{-5}{5}=-1[/tex]
Slope of BC, [tex]m_{2}=\frac{5-1}{9-2}=\frac{4}{7}[/tex]
[tex]tan\theta =\frac{m_{1}-m_{2}}{1+m_{1}m_{2}}[/tex]
[tex]tan\theta =\frac{(-1)-(\frac{4}{7})}{1+(-1)(\frac{4}{7})}=\frac{\frac{-11}{7}}{1-\frac{4}{7}}=\frac{\frac{-11}{7}}{\frac{3}{7}}=\frac{-11}{7}\times \frac{7}{3}=-\frac{11}{3}=-3.67[/tex]
[tex]\theta =tan^{-1}(-3.67)=74.75[/tex]
Since angle between them [tex]tan\theta[/tex] is negative that means angle theta will be obtuse angle.
So the angle between AB and BC = (180 - 74.75) = 105.26°
Therefore Option C. 105.26° is the answer.
Answer:
The correct answers are:
A) (50)^1/2
B) (65)^1/2
D) (145)^1/2
C) 105.26
Step-by-step explanation:
I got it right on the Edmentum test.
