Question

question 9 of 10
fill in the blank. in the triangle below, x = ____. round your answer to two decimal places.
triangle with right angle, one leg 35, angle 42° at top, x as horizontal leg, y as hypotenuse, z° at left
answer here

Explanation:

Step1: Identify the trigonometric ratio

We have a right - triangle with one angle of \(42^{\circ}\), the adjacent side to the \(42^{\circ}\) angle is \(35\) and the opposite side is \(x\). We can use the tangent function, which is defined as \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 42^{\circ}\), opposite \(=x\) and adjacent \( = 35\). So, \(\tan(42^{\circ})=\frac{x}{35}\).

Step2: Solve for \(x\)

To find \(x\), we can multiply both sides of the equation \(\tan(42^{\circ})=\frac{x}{35}\) by \(35\). So, \(x = 35\times\tan(42^{\circ})\). We know that \(\tan(42^{\circ})\approx0.9004\). Then \(x=35\times0.9004 = 31.514\approx31.51\) (rounded to two decimal places).

Answer:

\(31.51\)