Please answer this question. The answer is 2.77cm but my teacher wants a two triangle solution.

9514 1404 393

  5.69 cm

Step-by-step explanation:

The mnemonic SOH CAH TOA can remind you of the relationships between angles and sides in a right triangle. Here, the useful ones are ...

  Cos = Adjacent/Hypotenuse

  Sin = Opposite/Hypotenuse

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Using the first of these, we can find GD:

  cos(52°) = GC/GD

  GD = GC/cos(52°)

Using the second of these, we can find GH:

  sin(64°) = GH/GD

  GH = GD·sin(64°)

Substituting for GD, we find ...

  GH = GC·sin(64°)/cos(52°)

  GH ≈ (3.9 cm)(0.8988/0.6157)

  GH ≈ 5.69 cm

Additional comment

The length 2.77 cm given in your question is the approximate length of DH. That solution is DH = (3.9 cm)·cos(64°)/cos(52°) ≈ 2.7769 cm ≈ 2.78 cm.

Problems of this nature tend to be formulated different ways, so the specific answer will depend on the specific question. Angles and lengths and requested information may vary, even though the picture looks very similar. Read all the words.