Final answer:
The value of tan(49°) is 0.
Step-by-step explanation:
To find the value of tan(49°), we can use the tangent function which is defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle. In this case, the opposite side is unknown, but the adjacent side is 1. In a right triangle with an angle of 49°, we can use the Pythagorean theorem to find the length of the hypotenuse, which is √(1^2 + (opposite side)^2). Then, we can use the tangent function to find the value of tan(49°) by dividing the length of the opposite side by the length of the adjacent side.
Using the Pythagorean theorem, we have √(1^2 + (opposite side)^2) = √(1 + (opposite side)^2) = hypotenuse. Let's call the length of the opposite side y and solve the equation: √(1 + y^2) = hypotenuse. Squaring both sides of the equation, we get 1 + y^2 = hypotenuse^2. Subtracting 1 from both sides, we have y^2 = hypotenuse^2 - 1. Taking the square root of both sides, we get y = √(hypotenuse^2 - 1). Now, we can use the tangent function tan(49°) = y/1 = y to find the value of tan(49°).
Solving for y, we have y = √(hypotenuse^2 - 1) = √(1^2 - 1) = √0 = 0. Therefore, the value of tan(49°) is 0.