A small airplane takes off from point A and continues to climb upward in a straight line, as shown in the diagram. What is the plane’s distance from point A when it reaches point C?
Point A going up is 5600 ft. Going across is 5200 ft.
Point B across is 6500 ft. Going up is a ? . THE ANSWER TO CHOOSE FROM ARE:
A.6900
B.7000
C.11636
D,12600
E.13400
is d
To find the distance from point A to point C, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, we can treat the vertical distance from A to C as one side of the triangle, and the horizontal distance from A to C as the other side. The diagonal distance from A to C will be the hypotenuse.
Looking at the given information, we know that the vertical distance from A to B is 5600 ft, and the horizontal distance from A to B is 5200 ft. We also know that the horizontal distance from B to C is 6500 ft.
To find the vertical distance from B to C, we can use similar triangles. Since the ratio of the vertical distance to the horizontal distance is the same for both AB and BC (5600 ft / 5200 ft), we can set up the following proportion:
(Vertical distance from B to C) / 6500 ft = 5600 ft / 5200 ft
Cross-multiplying, we get:
(Vertical distance from B to C) = (5600 ft / 5200 ft) * 6500 ft
Simplifying, we get:
(Vertical distance from B to C) ≈ 7000 ft
Now that we have the vertical distance from A to C (5600 ft + 7000 ft = 12600 ft) and the horizontal distance from A to C (5200 ft + 6500 ft = 11700 ft), we can apply the Pythagorean theorem:
(Distance from A to C)² = (Vertical distance from A to C)² + (Horizontal distance from A to C)²
(Distance from A to C)² = (12600 ft)² + (11700 ft)²
Calculating the values, we find:
(Distance from A to C) ≈ 16636 ft
Therefore, the plane's distance from point A when it reaches point C is approximately 16636 ft. None of the given multiple-choice options match this answer exactly, so there may be an error in the provided answer options.