Question

a right triangle with one angle 45 degrees, one leg length 36, and the hypotenuse length x.

Explanation:

Step1: Identify trigonometric ratio

We use cosine: $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$

Step2: Substitute known values

$\cos(43^\circ) = \frac{36}{x}$

Step3: Rearrange to solve for $x$

$x = \frac{36}{\cos(43^\circ)}$

Step4: Calculate the value

Use $\cos(43^\circ) \approx 0.7314$, so $x \approx \frac{36}{0.7314} \approx 49.2$

Answer:

$x \approx 49.2$