Plz help me im stuck
1 answer:
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Answer:68.3 degrees
Step-by-step explanation:
The diagram of the triangle ABC is shown in the attached photo. We would determine the length of side AB. It is equal to a. We would apply the cosine rule which is expressed as follows
c^2 = a^2 + b^2 - 2abCos C
Looking at the triangle,
b = 75 miles
a = 80 miles.
Angle ACB = 180 - 42 = 138 degrees. Therefore
c^2 = 80^2 + 75^2 - 2 × 80 × 75Cos 138
c^2 = 6400 + 5625 - 12000Cos 138
c^2 = 6400 + 5625 - 12000 × -0.7431
c^2 = 12025 + 8917.2
c = √20942.2 = 144.7
To determine A, we will apply sine rule
a/SinA = b/SinB = c/SinC. Therefore,
80/SinA = 144.7/Sin 138
80Sin 138 = 144.7 SinA
SinA = 53.528/144.7 = 0.3699
A = 21.7 degrees
Therefore, theta = 90 - 21.7
= 68.3 degees
Correct question with correct options has been attached
Answer:
37
Step-by-step explanation:
Let C represent those dressed as heroes and let B represent those wearing mask
Thus;
n(C) = 39
n(D) = 45
We are told that 21 entrants were dressed as heroes wearing a mask.
Thus; n(C n D) = 21
We are also told that there were a total of 100 entries.
Thus, n(T) = 100
Now, number of entrants neither dressed as heroes nor wearing a mask is given by;
n(T) - n(C u D)
n(C u D) = n(C) + n(D) - n(C n D)
n(C u D) = 39 + 45 - 21
n(C u D) = 63
Thus;number of entrants neither dressed as heroes nor wearing a mask is: 100 - 63 = 37
