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Suppose that we know that a=5cm, b=5cm, and angle A=53o in a certain triangle. According to the Law of Sines,a) angle B must have an approximate measure of 48 degreesb) angle B must be obtusec) there are two triangles which meet the criteriad) there is exactly one triangle which meets the criteria

Respuesta :

Answer:

B = 53°

C = 74°

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The correct option for Suppose that we know that a=5cm, b=5cm, and angle A=53o in a certain triangle. According to the Law of Sines D. There is exactly one triangle that meets the criteria.

Given:

a = 5, b = 5,  A = 53°

⇒ a/sin A = b/sin B ⇒ Sin B = Sin A

                               ⇒ B = A (or) 180-A

                               ⇒ B = 53° (or) 127°

B = 53°:

           C = 180-A-B = 0 (not possible)

     

    ⇒ B = 53°, C = 74° ⇒ C = (Sin C)  (b/sin B) ≅ 6.02 cm

In which cases, can we use the law of sines?

Generally, the law of sines is used to solve the triangle, when we know two angles and one side or two angles and one included side. It means that the law of sines can be used when we have ASA (Angle-Side-Angle) or AAS (Angle-Angle-Side) criteria.

Learn more about the law of sines here https://brainly.com/question/27174058

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