Question

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

Answer 1

SOLUTION

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

$\begin{gathered} \text{Since we know the adjacent and hypotenuse, we use the cos function.} \\ \cos\theta=\frac{adjacent}{hypotenuse} \end{gathered}$

STEP 4: Substitute the values and solve for x

$\begin{gathered} cos32=\frac{12}{x} \\ By\text{ cross multiplication,} \\ x\times cos32=12 \\ Divide\text{ both sides by cos 32} \\ x=\frac{12}{\cos32} \\ x=14.15014084 \\ x\approx14.2 \end{gathered}$

Hence, the value of x is 14.2