Question

PLS HELP EMERGENCY I NEED U

Answer 1

1. sin∠EDA is equal to sin∠EBC

2. sin∠CEB is not equal to sin∠EBC

3. cos∠BEC is equal to sin∠EBC

4. cos∠ADE is not equal to sin∠EBC

5. sin(90 - m∠EBC) is not equal to sin∠EBC

6. cos(90 - m∠EDA) is equal to sin∠EBC

Explanation:

From inspection of the given diagram, ∠EAD = ∠ECB = 90°.

According to the vertical angles theorem, ∠BEC = ∠DEA.

According to AA similarity theorem, ΔADE ~ ΔCBE

Therefore, ∠EDA = ∠EBC.

This means that:

• sin∠EDA is equal to sin∠EBC
• sin∠CEB is not equal to sin∠EBC

`\boxed{\begin{minipage}{9.4 cm}\underline{Trigonometric ratios} \\\\$\sf \sin(\theta)=(O)/(H)\quad\cos(\theta)=(A)/(H)\quad\tan(\theta)=(O)/(A)$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}`

Since cos∠BEC = CE/BE and sin∠EBC = CE/BE then:

• cos∠BEC is equal to sin∠EBC.

As ∠BEC ≠ ∠ADE then:

• cos∠ADE is not equal to sin∠EBC.

As sin(90° - x) = cos(x) then sin(90 - m∠EBC) = cos∠EBC.

As cos∠EBC ≠ sin∠EBC then:

• sin(90 - m∠EBC) is not equal to sin∠EBC

As cos(90° - x) = sin(x) then cos(90 - m∠EDA) = sin∠EDA.

As sin∠EDA = sin∠EBC then cos(90 - m∠EDA) = sin∠EBC.

Hence:

• cos(90 - m∠EDA) is equal to sin∠EBC.