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Iteru [2.4K]
2 years ago
11

Find all the missing elements : C=120degrees b= 5 c=11

Mathematics
1 answer:
mezya [45]2 years ago
5 0

Answer:

A = 36.8°

B = 23.2°

a = 7.6

Step-by-step explanation:

Given:

C = 120°

b = 5

c = 11

Required:

Find A, B, and a.

Solution:

✔️To find B, apply the Law of Sines

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

Plug in the values

\frac{sin(B)}{5} = \frac{sin(120)}{11}

Cross multiply

Sin(B)*11 = sin(120)*5

Divide both sides by 11

sin(B) = \frac{sin(120)*5}{11}

sin(B) = \frac{sin(120)*5}{11}

Sin(B) = 0.3936

B = sin^{-1}(0.3936)

B = 23.1786882° ≈ 23.2° (nearest tenth)

✔️Find A:

A = 180° - (B + C) (sum of triangle)

A = 180° - (23.2° + 120°)

A = 36.8°

✔️To find a, apply the Law of sines:

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

Plug in the values

\frac{sin(36.8)}{a} = \frac{sin(23.2)}{5}

Cross multiply

a*sin(23.2) = 5*sin(36.8)

Divide both sides by sin(23.2)

a = \frac{5*sin(36.8)}{sin(23.2)

a = 7.60294329 ≈ 7.6 (nearest tenth)

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