answer:To find the distance between the person and the building, we can use the tangent function in trigonometry. The tangent function relates the angle of elevation, the opposite side (height of the building), and the adjacent side (distance between the person and the building) in a right triangle. Let's denote the distance between the person and the building as x. We are given the angle of elevation (60 degrees) and the height of the building (50 feet). We can set up the equation using the tangent function: tan(60) = opposite side / adjacent side tan(60) = 50 / x Now, we can solve for x: x = 50 / tan(60) The tangent of 60 degrees is equal to the square root of 3: x = 50 / √3 To rationalize the denominator, we can multiply the numerator and denominator by the square root of 3: x = (50 * √3) / (√3 * √3) x = (50 * √3) / 3 Now, we can approximate the value of x: x ≈ (50 * 1.732) / 3 x ≈ 86.6 / 3 x ≈ 28.87 Rounding to the nearest tenth, the distance between the person and the building is approximately 28.9 feet.

answer:To solve this problem, we can use the tangent function in trigonometry. Let's denote the height of the flag pole as h meters, and the horizontal distance between the building and the flag pole as d meters. We can form a right triangle with the building, the flag pole, and the ground. The angle of elevation of the telescope to the top of the flag pole is 35 degrees. So, we have: tan(35°) = (h - 20) / d We need to find the height of the flag pole (h), but first, we need to find the horizontal distance (d) between the building and the flag pole. To find d, we can use the complementary angle (90° - 35° = 55°) and the height of the building (20 meters). Using the tangent function again: tan(55°) = 20 / d Now, we can solve for d: d = 20 / tan(55°) d ≈ 15.02 meters Now that we have the value of d, we can find the height of the flag pole (h) using the tangent function with the angle of elevation (35°): tan(35°) = (h - 20) / 15.02 Now, solve for h: h - 20 = 15.02 * tan(35°) h - 20 ≈ 15.02 * 0.7002 h - 20 ≈ 10.52 h ≈ 30.52 meters So, the height of the flag pole from the ground is approximately 30.52 meters.

answer:To find the height of the building, we can use the tangent function in trigonometry. The tangent of an angle in a right triangle is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. In this case, the angle of elevation is 60 degrees, the side adjacent to the angle is the distance from the student to the building (20 meters), and the side opposite the angle is the height of the building (which we want to find). We can set up the equation: tan(60°) = height / 20 The tangent of 60 degrees is equal to the square root of 3, so: √3 = height / 20 Now, we can solve for the height: height = 20 * √3 ≈ 20 * 1.732 ≈ 34.64 Rounding to the nearest meter, the height of the building is approximately 35 meters.

answer:We can solve this problem using trigonometry. We have a right triangle with the building as the height, the distance from the base of the building to the point on the ground as the base, and the angle of elevation as 60 degrees. We can use the tangent function to find the distance from the base of the building to the point on the ground. The tangent function is defined as: tan(angle) = opposite side / adjacent side In this case, the opposite side is the height of the building (50 meters), and the adjacent side is the distance from the base of the building to the point on the ground, which we'll call "x". tan(60°) = 50 / x To find x, we can rearrange the equation: x = 50 / tan(60°) Now, we can plug in the value of tan(60°), which is √3: x = 50 / √3 To rationalize the denominator, we can multiply the numerator and denominator by √3: x = (50 * √3) / (3) x ≈ 28.87 meters So, the distance from the base of the building to the point on the ground is approximately 28.87 meters.