Question

Solve for the triangle where there is a question mark!

Answer 1

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

STEP 1: Label the right-angled triangle

STEP 2: Write the trigonometry ratios

`\begin{gathered} \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: Write the given values to decide which ratio to use

Let the part with the question be represented by m

`\begin{gathered} \text{adjacent}=7,\text{hypotenuse}=12,m=\text{?} \\ U\sin g\text{ the cos ratio from step 2;} \\ \cos m=(7)/(12) \\ m=\cos ^(-1)((7)/(12))=\cos ^(-1)0.5833333333 \\ m=54.31466529 \\ m\approx54.31 \end{gathered}`

Therefore, the value of mising angle labelled m is approximately 54.31 degrees