Question

7, a right triangle with one angle 72°, hypotenuse 10, and one leg y (the other leg is adjacent to the 72° angle)

Explanation:

Step1: Identify trigonometric ratio

We use the tangent function, since we have the opposite side ($10$) to the $72^\circ$ angle, and $y$ is the adjacent side. The tangent of an angle is $\frac{\text{opposite}}{\text{adjacent}}$.
$\tan(72^\circ) = \frac{10}{y}$

Step2: Rearrange to solve for $y$

Isolate $y$ by rearranging the equation: $y = \frac{10}{\tan(72^\circ)}$

Step3: Calculate the value

Using $\tan(72^\circ) \approx 3.0777$, substitute and compute:
$y \approx \frac{10}{3.0777} \approx 3.25$

Answer:

$y \approx 3.25$