Answer:
43.531
Step-by-step explanation:
This problem needs the law of cosines since the three sides of the triangle are involved as well as one angle. The law of cosines is:
c^2 = a^2 + b^2 - 2ab*cos(C)
Where the lowercase letters are side values and capital letters are angle values. Just in case I will mention side a is the one with a length of 14, side b is 20 and c = 12.
Since it is asking for angle A instead of angle C we can rewrite the law of cosines to fit that, basically just rearranging the letters.
a^2 = c^2 + b^2 - 2cb*cos(A)
Now we just plug in and solve.
14^2 = 12^2 + 20^2 - 2*12*20*cos(A)
Rearrange to get A by itself
![\frac{14^2-12^2-20^2}{-2*12*20}=cos(A)](https://tex.z-dn.net/?f=%5Cfrac%7B14%5E2-12%5E2-20%5E2%7D%7B-2%2A12%2A20%7D%3Dcos%28A%29)
Now we take the inverse cosine, or arccos of both sides to get our answer.
![arccos(\frac{14^2-12^2-20^2}{-2*12*20})=A](https://tex.z-dn.net/?f=arccos%28%5Cfrac%7B14%5E2-12%5E2-20%5E2%7D%7B-2%2A12%2A20%7D%29%3DA)
Let me know if there is something in my explanation you don't understand.
The consecutive positive integers would be: x and (x+1),
We would have to solve the following equation to find these numbers:
x(x+1)-[x+(x+1)]=29
x²+x-2x-1=29
x²-x-30=0
x=[1⁺₋√(1+120)]/2
x=(1⁺₋11)/2
We have two possible solutions:
x₁=(1-11)/2=-5 then: (x+1)=-5+1=-4 This is not the solution.
x₂=(1+11)/2=6 then: (x+1)=6+1=7 This solution is right.
Answer: the numbers would be 6 and 7.
Answer:
145°
Step-by-step explanation:
The angle is 90°+55°=145°
Answer:
1260°
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Geometry</u>
- Sum of Angles: 180(n - 2)
Step-by-step explanation:
<u>Step 1: Define</u>
Number of sides <em>n</em> = 9
<u>Step 2: Find</u>
- Substitute: 180(9 - 2)
- Subtract: 180(7)
- Multiply: 1260°
Answer:
Yes
Step-by-step explanation:
I had this exact question.