Question

Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. B = 15° C = 113° b = 49

Answer 1

Answer:

  A = 52°, a = 149.2, c = 174.3

Step-by-step explanation:

Technology is useful for this. Many graphing calculators can solve triangles for you. The attachment shows a phone app that does this, too.

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The Law of Sines can give you the value of c, so you can choose the correct answer from those offered.

  c = sin(C)·b/sin(B) = sin(113°)·49/sin(15°) ≈ 174.271 ≈ 174.3 . . . . . third choice

Answer 2

Answer:

A = 52°, a = 149.2, c = 174.3

Step-by-step explanation:

We are given the following two known angles and one known side length for a triangle and we are to find the rest of the side lengths and angle:

B = 15° C = 113° b = 49

A = 180 - ( 15 + 113) = 52°

For finding the side lengths, we can use the sine rule:

$\frac{a}{sin(A)}=\frac{b}{sin(B)}$

$\frac{a}{sin(52)} =\frac{49}{sin(15)}$

a = 149.2

$\frac{c}{sin(C)}=\frac{b}{sin(B)}$

$\frac{c}{sin(113)} =\frac{49}{sin(15)}$

c = 174.3