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ser-zykov [4K]
3 years ago
9

List the angles of the triangle in order from smallest to largest. In triangle Upper A Upper C Upper B, line segment Upper A Upp

er C has length 4.3, line segment Upper B Upper C has length 5.9, and line segment Upper B Upper A has length 3.5. A C B 5.9 4.3 3.5 Choose the correct order of the angles from smallest to largest.
Mathematics
1 answer:
Ulleksa [173]3 years ago
8 0

Answer:

C = 36.0

B = 46.2

A = 97.8

Step-by-step explanation:

Given

\triangle ABC

AC = 4.3

BC = 5.9

BA = 3.5

Required

List the angles from smallest to largest

The given parameters is illustrated with the attached image.

AC = 4.3 -- b

BC = 5.9 --- a

BA = 3.5 --- c

This question will be solved using cosine rule

To calculate A, we have:

a^2 = b^2 + c^2 -2bc\ cos(A)

So, we have:

5.9^2 = 4.3^2 + 3.5^2 - 2 * 4.3 * 3.5 * \cos(A)

34.81 = 18.49+ 12.25 - 30.10*  \cos(A)

Collect like terms

34.81 - 18.49- 12.25 = - 30.10*  \cos(A)

4.07 = - 30.10*  \cos(A)

Make cos(A) the subject

\cos(A) = -\frac{4.07}{30.10}

\cos(A) = -0.1352

Take arccos of both sides

A = cos^{-1}(-0.1352)

A = 97.8

Solving for B, we have:

b^2 = a^2 + c^2 -2ac\ cos(B)

This gives:

4.3^2 = 5.9^2 + 3.5^2 -2*5.9*3.5\ cos(B)

18.49 = 34.81+ 12.25 -41.30 *\cos(B)

Collect like terms

18.49 - 34.81 - 12.25 = -41.30 *\cos(B)

-28.57 = -41.30 *\cos(B)

Solve for cos(B)

\cos(B) = \frac{-28.57}{-41.30}

\cos(B) = 0.6918

Take arccos of both sides

B = cos^{-1}(0.6918)

B = 46.2

To solve for C, we make use of:

A + B + C = 180 --- angles in a triangle

97.8 + 46.2 + C = 180

Collect like terms

C = - 97.8 - 46.2 + 180

C = 36.0

So, we have:

C = 36.0

B = 46.2

A = 97.8

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