Questions: b) Find the perimeter.

Solution Steps

We are given a right triangle with angle \(41^{\circ}\) and hypotenuse 26 m. Let the adjacent side be \(x\). We can use cosine to find the length of the adjacent side: \(\cos(41^{\circ}) = \frac{x}{26}\) \(x = 26 \cos(41^{\circ})\) \(x \approx 26 \times 0.7547\) \(x \approx 19.62\) m

Let the opposite side be \(y\). We can use the sine function to find the length of the opposite side: \(\sin(41^{\circ}) = \frac{y}{26}\) \(y = 26 \sin(41^{\circ})\) \(y \approx 26 \times 0.6561\) \(y \approx 17.06\) m

The perimeter of the triangle is the sum of the lengths of all three sides: Perimeter = adjacent + opposite + hypotenuse Perimeter \(= x + y + 26\) Perimeter \(\approx 19.62 + 17.06 + 26\) Perimeter \(\approx 62.68\) m

Final Answer