How do you use law of sines to solve the triangle given A=24 degrees, a=8.5, c=10.6?

Answer 1

# C = 30.5° and B = 125.5° and b = 17.0#

In order to use the Sine Rule you have to know the size of one angle and the length of its opposite side. A third measurement can be either another side or an angle.

#(sin A)/a = (sin B)/b = (sin C)/c" "# or #" " a/sin A= b/ sin B = c/sin C#
We have angle A, and sides a and c.#rArr# we can find angle C. I prefer to have the unknown at the top of the left side.
#sin C/10.6 = sin 24/8.5 " "rArr" " sin C = (10.6 xxsin 24)/8.5#

Note than Sin values are always from 0 to 1, so we are expecting an answer of 0....... If this does not happen there is an error.

#Sin C=0.5.722...." find arcsin, " (sin)^-1#
#:. C = 30.5°#

To solve the triangle means to find all the unknown sides and angles. We need to find angle B and side b

#"Angle B" = 180° - 24° - 30.5° = 125.5° " (angles in a triangle)"#
#b/sin 125.5 = 8.5/sin 24 " "rArr" " b = (8.5 xxsin 125.5)/sin 24#
#b = 17.0#
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Answer 2

To use the Law of Sines to solve the triangle given angle A = 24 degrees, side a = 8.5, and side c = 10.6, you can follow these steps:

  1. Use the Law of Sines to find angle C: [\frac{\sin C}{c} = \frac{\sin A}{a}] [\sin C = \frac{c \times \sin A}{a}] [\sin C = \frac{10.6 \times \sin 24^\circ}{8.5}] [C = \sin^{-1} \left(\frac{10.6 \times \sin 24^\circ}{8.5}\right)]

  2. Use the fact that the sum of angles in a triangle is 180 degrees to find angle B: [B = 180^\circ - A - C]

  3. Once you have angles B and C, you can use the Law of Sines again to find side b: [\frac{\sin B}{b} = \frac{\sin A}{a}] [b = \frac{a \times \sin B}{\sin A}]

  4. Plug in the known values to find side b: [b = \frac{8.5 \times \sin B}{\sin 24^\circ}]

  5. After finding angles B and C and side b, you will have solved the triangle.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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