Type your answer If the side adjacent to an angle has a length of 5 and the tangent of the angle equals 1 , what is the length of the side opposite the angle? (20 out of 2

To find the length of the side opposite the angle when the adjacent side is 5 and the tangent of the angle is 1, you can use the definition of tangent in a right triangle. Tangent of an angle in a right triangle is equal to the ratio of the length of the opposite side to the length of the adjacent side. Since \( \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \), and with \( \tan(\theta) = 1 \), you have: \[ 1 = \frac{\text{opposite}}{5} \] Therefore, the length of the opposite side is also 5. If you find yourself confused by tangent problems, remember that \(\tan(45^\circ) = 1\), which aligns perfectly with your situation! Always visualize or sketch the triangles—geometry doesn't have to be a bore. Drawing helps clarify relationships between sides and angles.