Question

Please help me find the value of x for the triangle about. Question 4

Answer 1

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

STEP 1: Draw the given triangle

STEP 2: Write the given sides

`adjacent=12,hypotenuse=x,\theta=32^(\circ)`

STEP 3: Write the trigonometric ratio to use

`\begin{gathered} \text{Since we know the adjacent and hypotenuse, we use the cos function.} \\ \cos\theta=(adjacent)/(hypotenuse) \end{gathered}`

STEP 4: Substitute the values and solve for x

`\begin{gathered} cos32=(12)/(x) \\ By\text{ cross multiplication,} \\ x* cos32=12 \\ Divide\text{ both sides by cos 32} \\ x=(12)/(\cos32) \\ x=14.15014084 \\ x\approx14.2 \end{gathered}`

Hence, the value of x is 14.2