Solve the right triangle with the given side and angle alpha =12^circ ,c=26 aapprox square (Do not round until the final answer.Then round to the nearest tenth as needed.) bapprox square (Do not round until the final answer.Then round to the nearest tenth as needed.) beta approx square ^circ (Do not round until the final answer.Then round to the nearest whole number as needec

To solve the right triangle with the given angle and side, we can use trigonometric ratios.<br /><br />Given:<br />$\alpha = 12^{\circ}$<br />$c = 26$<br /><br />We need to find the lengths of sides $a$ and $b$, and the measure of angle $\beta$.<br /><br />Step 1: Use the sine function to find the length of side $a$.<br />$\sin(\alpha) = \frac{a}{c}$<br />$a = c \cdot \sin(\alpha)$<br />$a = 26 \cdot \sin(12^{\circ})$<br />$a \approx 5.3$<br /><br />Step 2: Use the cosine function to find the length of side $b$.<br />$\cos(\alpha) = \frac{b}{c}$<br />$b = c \cdot \cos(\alpha)$<br />$b = 26 \cdot \cos(12^{\circ})$<br />$b \approx 25.4$<br /><br />Step 3: Use the fact that the sum of angles in a triangle is $180^{\circ}$ to find the measure of angle $\beta$.<br />$\beta = 90^{\circ} - \alpha$<br />$\beta = 90^{\circ} - 12^{\circ}$<br />$\beta \approx 78^{\circ}$<br /><br />Therefore, the solutions are:<br />$a \approx 5.3$<br />$b \approx 25.4$<br />$\beta \approx 78^{\circ}$