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Child: b=5cm

<A=64⁰
<B=38⁰
Dit: a.a
b.c
c. <c
questions about the law of sines and cosines


User Nico Adams
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1 Answer

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Explanation:

Based on the given information:

Side b = 5 cm

Angle A = 64 degrees

Angle B = 38 degrees

To solve for the missing values, we can use the Law of Sines and the Law of Cosines.

a. To find side a using the Law of Sines:

We can use the formula: sin(A) / a = sin(B) / b

sin(64°) / a = sin(38°) / 5

To solve for a, we can rearrange the equation:

a = (sin(64°) * 5) / sin(38°)

b. To find side c using the Law of Cosines:

We can use the formula: c^2 = a^2 + b^2 - 2ab * cos(C)

First, we need to find angle C using the fact that the sum of angles in a triangle is 180 degrees:

C = 180° - A - B

C = 180° - 64° - 38°

Once we have angle C, we can substitute the known values into the Law of Cosines equation:

c^2 = a^2 + b^2 - 2ab * cos(C)

Now, we can solve for c.

c. To find angle C using the Law of Sines:

We can use the formula: sin(C) / c = sin(A) / a

sin(C) / c = sin(64°) / a

To solve for angle C, we can rearrange the equation:

C = arcsin((sin(64°) * c) / a)

Please note that the specific calculations will depend on the values of a, c, and the trigonometric functions used.

User Achille
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