Question

solve for x. round to the nearest tenth, if necessary.
triangle with right angle at v, angle at w is 32 degrees, hypotenuse wu is 4.9, side wv is x
answer attempt 1 out of 2
x = |

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle \( \triangle WVU\), we know the hypotenuse \(WU = 4.9\) and the adjacent side to the angle \(32^{\circ}\) is \(x\). The cosine ratio is defined as \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 32^{\circ}\), adjacent \(=x\), and hypotenuse \(=4.9\). So, \(\cos(32^{\circ})=\frac{x}{4.9}\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\cos(32^{\circ})=\frac{x}{4.9}\) by \(4.9\). We get \(x = 4.9\times\cos(32^{\circ})\).
We know that \(\cos(32^{\circ})\approx0.848\). Then \(x = 4.9\times0.848\).
Calculate \(4.9\times0.848=(5 - 0.1)\times0.848=5\times0.848-0.1\times0.848 = 4.24 - 0.0848=4.1552\approx4.2\)

Answer:

\(x = 4.2\)