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Solve the right triangle

Solve the right triangle-example-1

1 Answer

6 votes

Answer:

  • AC = 1.5 cm
  • A = 61°
  • B = 29°

Explanation:

You want the missing side and the angles for the right triangle with leg BC = 2.7 cm and hypotenuse AB = 3.1 cm.

Cosine

The cosine of angle B is given by ...

Cos = Adjacent/Hypotenuse

cos(B) = CB/AB = 2.7/3.1

Then the angle is ...

B = arccos(2.7/3.1) ≈ 29.429°

B ≈ 29°

Angle A is the complement of angle B:

A = 90° -29°

A = 61°

Sine

The sine ratio is ...

Sin = Opposite/Hypotenuse

Then side AC can be found from ...

sin(B) = AC/AB

AC = AB·sin(B) = 3.1·sin(29.429°) ≈ 1.523

AC ≈ 1.5 . . . . cm

The triangle solution is ...

  • A = 61°
  • B = 29°
  • AC = 1.5 cm

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Additional comment

The mnemonic SOH CAH TOA is intended to help you remember the trig ratios above, in addition to ...

Tan = Opposite/Adjacent

Solve the right triangle-example-1
User Hemdi
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