7900 79 times 100 ------------
Remark
You must use the sin law to find this.
![\dfrac{Sin(75)}{22} = \dfrac{Sin(x)}{12}](https://tex.z-dn.net/?f=%20%5Cdfrac%7BSin%2875%29%7D%7B22%7D%20%3D%20%5Cdfrac%7BSin%28x%29%7D%7B12%7D%20%20%20)
Multiply through by 12
12 *
*12
![\dfrac{12*sin(75)}{22} = \text{sin(x)}](https://tex.z-dn.net/?f=%20%5Cdfrac%7B12%2Asin%2875%29%7D%7B22%7D%20%3D%20%5Ctext%7Bsin%28x%29%7D%20%20)
0.5269 = sin(x)
Now you have to use the inverse of the sine function.
Use your calculator for that
2nd F
sin-1
(0.5269)
= 31.79 degrees. <<<<<< Answer.
There sometimes is a second answer. I don't think there is in this case.
Answer:
33.3 % (Approx) percent of fish that Tom’s caught of the number of fish his son caught .
25% is the percent of the total amount Tom caught.
Step-by-step explanation:
Formula
![Percentage = \frac{Part\ value\times 100}{Total\ values}](https://tex.z-dn.net/?f=Percentage%20%3D%20%5Cfrac%7BPart%5C%20value%5Ctimes%20100%7D%7BTotal%5C%20values%7D)
Part First
As given
Tom caught 4 fish and his son caught 12 fish.
Here
Part value = 4
Total value = 12
Put in the formula
![Percentage = \frac{4\times 100}{12}](https://tex.z-dn.net/?f=Percentage%20%3D%20%5Cfrac%7B4%5Ctimes%20100%7D%7B12%7D)
![Percentage = \frac{400}{12}](https://tex.z-dn.net/?f=Percentage%20%3D%20%5Cfrac%7B400%7D%7B12%7D)
Percentage = 33.3 % (Approx)
Therefore the 33.3 % (Approx) percent of fish that Tom’s caught of the number of fish his son caught .
Second Part
As given
Tom caught 4 fish and his son caught 12 fish.
Total number of fish caught = 4 + 12
= 16
Part value = 4
Total value = 16
Put in the formula
![Percentage = \frac{4\times 100}{16}](https://tex.z-dn.net/?f=Percentage%20%3D%20%5Cfrac%7B4%5Ctimes%20100%7D%7B16%7D)
![Percentage = \frac{400}{16}](https://tex.z-dn.net/?f=Percentage%20%3D%20%5Cfrac%7B400%7D%7B16%7D)
Percentage = 25%
Therefore the 25% is the percent of the total amount Tom caught.
Answer:
Option D
Step-by-step explanation:
The questions which involve calculating the angles and the sides of a triangle either require the sine rule or the cosine rule. In this question, the two sides that are given are adjacent to each other and the given angle is the included angle. This means that the angle is formed by the intersection of the two lines. Therefore, cosine rule will be used to calculate the length of b. The cosine rule is:
b^2 = a^2 + c^2 - 2*a*c*cos(B).
The question specifies that a=42, B=120°, and c=35. Plugging in the values:
b^2 = 42^2 + 35^2 - 2(42)(35)*cos(120°).
Simplifying gives:
b^2 = 4459.
Taking square root on the both sides gives b = 66.78 (rounded to the two decimal places).
This means that the length of the third side is 66.78 units!!!