Question

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

Answer 1

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.

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

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

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

$x = 23.7~cm$