Question

In the accompanying diagram, what is sin E?
Please see image below (math)

Answer 1

`\sin E=(4)/(5)`

Explanation:

To find the value of sin E we can use the sine trigonometric ratio.

`\boxed{\begin{minipage}{9 cm}\underline{Sine trigonometric ratio} \\\\$\sf \sin(\theta)=(O)/(H)$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}`

From inspection of the given right triangle:

• The angle is E, so θ = E.
• The side opposite angle E is FG, so O = 4.
• The hypotenuse of the triangle is EF, so H = 5.

Substitute these values into the sine ratio:

`\sin E=(4)/(5)`