Question

How do you work out this problem

Answer 1

`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)`

Answer 2

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.