Question

Find the sine of angle Ø in the triangle below.

Answer 1

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Show the given right-angled triangle

STEP 2: Write the given values for the sides and the appropriate trigonemtric ratio to use

`\begin{gathered} \text{opposite}=\text{?,adjacent}=9,\text{hypotenuse}=15 \\ \sin \theta=\frac{\text{opposite}}{\text{hypotenuse}} \\ \cos \theta=\frac{\text{adjacent}}{\text{hypotenuse}} \\ \tan \theta=\frac{\text{opposite}}{\text{adjacent}} \end{gathered}`

STEP 3: Get the third side

Since we were to find the sine of the given angle, we need to find the opposite to allow us use the trig ratio in step 2

`\begin{gathered} U\sin g\text{ pythagoras theorem,} \\ \text{hypotenuse}^2=opposite^2+adjacent^2 \\ \text{hypotenuse}^2-adjacent^2=opposite^2 \\ By\text{ substitution,} \\ 15^2-9^2=opposite^2 \\ \text{opposite}^2=225-81=144 \\ \text{opposite}=\sqrt[]{144}=12 \end{gathered}`

STEP 4: Express the sine of the given angle

`\begin{gathered} \text{From step 2,} \\ \sin \theta=(opposite)/(hypotenuse) \\ \text{opposite}=12,\text{hypotenuse}=15 \\ By\text{ substitution,} \\ \sin \theta=(12)/(15) \end{gathered}`

Hence, the sine of the angle is 12/15