Question

3)
find the value of x in the right triangle, where one angle is 26°, the hypotenuse is 19, and x is one of the legs adjacent to the right angle.

Explanation:

Step1: Identify trigonometric ratio

For the $26^\circ$ angle, $x$ is the opposite side, and 19 is the adjacent side. Use tangent: $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$

Step2: Substitute known values

$\tan(26^\circ)=\frac{x}{19}$

Step3: Solve for $x$

$x = 19 \times \tan(26^\circ)$
Calculate $\tan(26^\circ)\approx0.4877$, so $x\approx19\times0.4877$

Answer:

$x\approx9.27$