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Goryan [66]
2 years ago
11

HELP PLEASE URGENT, ASAP. THIS IS GRADE 11 TRIGONOMETRY ILL GIVE THE BRAINLIEST!!!!!!!!!!!!

Mathematics
1 answer:
Darya [45]2 years ago
8 0

Answer:

1. \theta = 61.9^\circ

2. x = 23.7~cm

Step-by-step explanation:

Problem 1.

Use the Law of Sines.

This is SSA.

\dfrac{a}{\sin A} = \dfrac{c}{\sin C}

\dfrac{31.2~cm}{\sin 51^\circ} = \dfrac{35.4~cm}{\sin \theta}

\sin \theta = \dfrac{35.4~cm \times \sin 51^\circ}{31.2~cm}

\sin \theta = 0.88176

\theta = \sin^{-1} 0.88176

\theta = 61.9^\circ

Problem 2.

m<A + m<B + m<C = 180°

m<A + 67° + 58° = 180°

m<A = 55°

Use the Law of Sines.

\dfrac{a}{\sin A} = \dfrac{c}{\sin C}

\dfrac{x}{\sin 55^\circ} = \dfrac{24.5}{\sin 58^\circ}

x = \dfrac{\sin 55^\circ \times 24.5}{\sin 58^\circ}

x = 23.7~cm

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