Final answer:
To find the height of a right triangle with a 60-degree angle and a base of 4, use the tangent function: h = 4 * tan(60°) = 4√3. The height of the triangle is 4√3 units.
Step-by-step explanation:
To find the height of a right triangle where one angle measures 60 degrees and the base adjacent to this angle is 4 units, we can use trigonometry. Specifically, the sine function can be used, which in a right triangle is the ratio of the opposite side (the height we want to find) over the hypotenuse. However, we don't have the hypotenuse in this case but we do have the adjacent side to the 60-degree angle. So, we will use the tangent function which relates the opposite side over the adjacent side. The tangent of a 60-degree angle equals √3. Therefore, to find the height (h), we can set up the equation h = 4 * tan(60°) = 4 * √3. Since the exact value of tan(60°) is √3, we can calculate h = 4 * √3. This simplifies to h = 4√3 units, which is the height of the triangle.
The Pythagorean theorem could also be used if the hypotenuse was known. It relates the lengths of the two legs of a right triangle, a and b, to the length of the hypotenuse, c, using the equation a² + b² = c². However, since we only know one leg and the angle in this scenario, the trigonometric function is more suitable.