Question

calculate the unknown length. 4 m 56° ? m

Explanation:

Step1: Identify the trigonometric ratio

We know the hypotenuse (\(4\) m) and need to find the adjacent side to the \(56^{\circ}\) angle. Use the cosine ratio: \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\).

Step2: Substitute the values

Let the unknown length be \(x\). Then \(\cos(56^{\circ})=\frac{x}{4}\).

Step3: Solve for \(x\)

Multiply both sides by \(4\): \(x = 4\times\cos(56^{\circ})\).
Using a calculator (\(\cos(56^{\circ})\approx0.5592\)), \(x\approx4\times0.5592 = 2.2368\approx2.24\) (rounded to two decimal places).

Answer:

\(2.24\) m