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Consider a triangle ABC like the one below. Suppose that B=37°, C=26°, and b = 35. (The figure is not drawn to scale.) Solve the triangle.
Round your answers to the nearest tenth.
If there is more than one solution, use the button labeled "or".

Consider a triangle ABC like the one below Suppose that B37 C26 and b 35 The figure is not drawn to scale Solve the triangle Round your answers to the nearest t class=

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sqdancefan

Answer:

  • A = 117°
  • a = 51.8
  • c = 25.5

Step-by-step explanation:

You want the solution to triangle ABC with b=35, B=37°, C=26°.

Angle

The remaining angle is the supplement of the sum of the given angles:

  A = 180° -(37° +26°)

  A = 117°

Law of sines

The law of sines tells you side lengths are proportional to the sine of the opposite angle:

  b/sin(B) = a/sin(A) = c/sin(C)

  a = b/sin(B)·sin(A) = 35/sin(37°)·sin(117°)

  a ≈ 51.8

  c = b/sin(B)·sin(C) = 35/sin(37°)·sin(26°)

  c ≈ 25.5

The solution is A = 117°, a = 51.8, c = 25.5.

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Additional comment

When two angles are specified, there can be only one solution. There may be two solutions when two sides are specified and the given angle is opposite the shorter given side.

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