What is the angle of b?So first off, I know how to find the missing length of the leg of the triangle using the pythagorean theorem. 6 2 + b 2 = c 2 . 36 + b 2 = 100 100 − 36 = 64 64 = 8So angle angle A is going to be adjacent hypotenuse . cos ⁡ ( angle ) = adjacent hypotenuse cos ⁡ ( angle ) = 8 10 cos − 1 ⁡ ( 0.8 ) = 36.86989765 ∘ Here is where I run into my problem. So assuming that B is going to be opposite hypotenuse . sin ⁡ ( angle ) = 6 10 sin − 1 ⁡ ( 0.6 ) = 36.86989765 ∘ However, when I use the law of cosines I get the same answer for angle A, but a different angle for B, which comes out as 53.13. It would be greatly appreciated if someone could help me figure out where my mistakes are.

Question

What is the angle of b?So first off, I know how to find the missing length of the leg of the triangle using the pythagorean theorem.       6    2    +      b    2    =      c    2  .  36  +      b    2    =  100  100  −  36  =  64      64    =  8So angle angle A is going to be       adjacent    hypotenuse  .  cos  ⁡  (  angle  )  =      adjacent    hypotenuse    cos  ⁡  (  angle  )  =      8    10        cos          −      1        ⁡  (  0.8  )  =      36.86989765    ∘  Here is where I run into my problem. So assuming that B is going to be       opposite    hypotenuse  .  sin  ⁡  (  angle  )  =      6    10        sin          −      1        ⁡  (  0.6  )  =      36.86989765    ∘  However, when I use the law of cosines I get the same answer for angle A, but a different angle for B, which comes out as 53.13. It would be greatly appreciated if someone could help me figure out where my mistakes are.

Emilie Reeves · Accepted Answer

Explanation:B is   ∼      53.13          ∘      .When you took opposite by adjacent with regard to B, it should be:  sin  ⁡  (  B  )  =      8    10      ⟹    B  =      sin          −      1        ⁡      (          8      10        )    ≈      53.13    ∘  You took opposite/adjacent to be 6/10, when the side opposite to angle B is actually 8 units long. That&#039;s why you calculated it wrong the first time.

Find the missing length of the leg of the triangle using the pythagorean theorem. 6^2+b^2=c^2.

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