17) The line that is John is closer to certain but not exactly on certain so I'd say it's "likely"
18) Using that same example as the one above, if 0 means impossible, then 1 means certain. I'd place your label for Sara at 1.
19) Let s = sides of the square. There are 4 sides and all sides are equal so we can set up the equation 4s = 64. Divide both sides by 4. s = 16. Now add 2 to this. 16 + 2 = 18. The length of each side of the original square was 18.
20) If the scale is 1 cm : 1 meter and the height of the model is 16 cm, then the actual plane must be 16 meters.
21) 2x and 100 are supplementary angles meaning together they must add up to 180.
2x + 100 = 180
2x = 180 - 100
2x = 80
Divide both sides by 2
x = 40
22) Assuming 3x is supposed to be the right angle, right angles are 90 degrees.
3x = 90
Divide by 3 on both sides
x = 30.
Option B: 4.0 cm is the value of w
Explanation:
It is given that 
, 
, 
and 
Using the law of sines, we have,
Substituting the values, we have,
Cross multiplying, we get,
Simplifying, we have,
Dividing both sides by 0.515, we have,
Thus, the value of w is 4.0 cm
Hence, Option B is the correct answer.
Answer:
1.8 units.
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 the largest side of the triangle. The cosine rule is:
b^2 = a^2 + c^2 - 2*a*c*cos(B).
The question specifies that a=0.5, B=120°, and c=1.5. Plugging in the values:
b^2 = 0.5^2 + 1.5^2 - 2(0.5)(1.5)*cos(120°).
Simplifying gives:
b^2 = 3.25.
Taking square root on the both sides gives b = 1.8 (rounded to the nearest tenth).
This means that the length of the third side is 1.8 units!!!
There are no options to choose from but I hope this helps
