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How do you work out this problem

How do you work out this problem-example-1

2 Answers

3 votes

Answer:


sin(A) = (2)/(√(13) )=(2√(13) )/(13)


cos(A)=(3)/(√(13) ) =(3√(13))/(13)


tan(A)=(2)/(3)

Explanation:

So first we need to make sure we know the trig identities to solve this problem.


  • sin(\alpha )=(opposite)/(hypotenuse)

  • cos(\alpha )=(adjacent)/(hypotenuse)

  • tan(\alpha )=(opposite)/(adjacent)

Here we only have two legs of the triangle, so we will need to use the Pythagorean Theorem a² + b² = c² to solve for the missing leg, the hypotenuse in this case.

  • Solving for the hypotenuse, c, we get
    c = \sqrt{a^(2) +b^(2) }
  • Here a = 3 and b = 2, so plugging in these values to the equation we get:
    c= \sqrt{(3)^(2)+(2)^(2) } =√(9+4) =√(13)

Now we can use the trig identities to figure out the missing values for the problem


  • sin(A) = (2)/(√(13) )=(2√(13) )/(13)

  • cos(A)=(3)/(√(13) ) =(3√(13))/(13)

  • tan(A)=(2)/(3)
How do you work out this problem-example-1
User Tomwalsham
by
8.7k points
4 votes

Answer:

Sin A =
(2)/(3.6)

Cos A =
(3)/(3.6)

Tan A =
(2)/(3)

Explanation:

First of all, we will need to find the hypotenuse. We can do this using the Pythagoras theorem.


c^(2) = a^(2) + b^(2)

where a = 2 and b = 3,

solving for c we end up with 3.6.

Sin A =
(opp)/(hyp)

Cos A =
(adj)/(hyp)

Tan A =
(opp)/(hyp)

The line opposite to the angle A is 2 and the line adjacent to it is 3.

Filling in, we get the answer.

Hope this helps.

User Lannetta
by
7.4k points

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