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irga5000 [103]
3 years ago
6

Solve the triangle A=48 degrees, a= 32, b=27

Mathematics
1 answer:
abruzzese [7]3 years ago
8 0
\bf \textit{Law of sines}
\\ \quad \\
\cfrac{sin(\measuredangle A)}{a}=\cfrac{sin(\measuredangle B)}{b}=\cfrac{sin(\measuredangle C)}{c}\\\\
-----------------------------\\\\


\bf \cfrac{sin(48^o)}{32}=\cfrac{sin(B)}{27}\implies\cfrac{27sin(48^o)}{32}=sin(B)
\\\\\\
sin^{-1}\left[ \cfrac{27sin(48^o)}{32} \right]=sin^{-1}[sin(B)]\implies sin^{-1}\left[ \cfrac{27sin(48^o)}{32} \right]=\measuredangle B
\\\\\\
38.83\approx \measuredangle B
\\\\\\
\textit{now, we know angles A and B, angle is C is just 180-A-B}
\\\\\\
\measuredangle C = 180-48-38.83\implies C\approx 93.17^o

so, now we know the ∡C, so, let's use the law of sines to get side "c"

\bf \cfrac{sin(48^o)}{32}=\cfrac{sin(93.17^o)}{c}\implies c=\cfrac{32sin(93.17^o)}{sin(48^o)}

and surely you know how much that is
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A coin is tossed twice. What is the probability of getting a tail in the first toss and a tail in the second toss?
skelet666 [1.2K]

Answer:

<h2>1/4 Chances</h2><h2>25% Chances</h2><h2>0.25 Chances (out of 1)</h2>

Step-by-step explanation:

Two methods to answer the question.

Here are presented to show the advantage in using the product rule given above.

<h2>Method 1:Using the sample space</h2>

The sample space S of the experiment of tossing a coin twice is given by the tree diagram shown below

The first toss gives two possible outcomes: T or H ( in blue)

The second toss gives two possible outcomes: T or H (in red)

From the three diagrams, we can deduce the sample space S set as follows

          S={(H,H),(H,T),(T,H),(T,T)}

with n(S)=4 where n(S) is the number of elements in the set S

tree diagram in tossing a coin twice

The event E : " tossing a coin twice and getting two tails " as a set is given by

          E={(T,T)}

with n(E)=1 where n(E) is the number of elements in the set E

Use the classical probability formula to find P(E) as:

          P(E)=n(E)n(S)=14

<h2>Method 2: Use the product rule of two independent event</h2>

Event E " tossing a coin twice and getting a tail in each toss " may be considered as two events

Event A " toss a coin once and get a tail " and event B "toss the coin a second time and get a tail "

with the probabilities of each event A and B given by

          P(A)=12 and P(B)=12

Event E occurring may now be considered as events A and B occurring. Events A and B are independent and therefore the product rule may be used as follows

        P(E)=P(A and B)=P(A∩B)=P(A)⋅P(B)=12⋅12=14

NOTE If you toss a coin a large number of times, the sample space will have a large number of elements and therefore method 2 is much more practical to use than method 1 where you have a large number of outcomes.

We now present more examples and questions on how the product rule of independent events is used to solve probability questions.

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