Question

4, 16°, 37, x, right angle triangle

Explanation:

Step1: Identify the trigonometric relationship

We have a right triangle, and we know an angle of \(16^\circ\), the adjacent side to this angle is \(x\), and the hypotenuse is \(37\). The cosine of an angle in a right triangle is defined as \(\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}\). So, \(\cos(16^\circ)=\frac{x}{37}\).

Step2: Solve for \(x\)

To find \(x\), we can multiply both sides of the equation by \(37\). So, \(x = 37\times\cos(16^\circ)\).

First, calculate \(\cos(16^\circ)\). Using a calculator, \(\cos(16^\circ)\approx0.9613\).

Then, multiply by \(37\): \(x\approx37\times0.9613\approx35.57\).

Answer:

\(x\approx35.57\) (If we need to round to a certain decimal place or use more precise calculation, the result may vary slightly, but this is the approximate value.)