In right triangle ABC, angle C=90 degrees, AC = 3 and CB =4. If D is on segment AB and DB = 2, find the distance from D to C.
AB is the hypotenuse, the length of which is sqrt (3^2 + 4^2) = 5 since this is a right triangle. CD is a line from the right angle corner to a point on the hypotenuse. You can gets its length by applying the law of cosines on smaller triangle BCD. You know the lengths of BD and BC and the included angle B cosine (which is 4/5)
To find the distance from point D to point C in a right triangle, we can use the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (in this case, side AC) is equal to the sum of the squares of the lengths of the other two sides.
Given that angle C is 90 degrees, we have a right triangle ABC with AC as the hypotenuse. We are given that AC = 3 and CB = 4. To find the length of AB (the third side of the triangle), we can use the Pythagorean Theorem:
AB^2 = AC^2 - CB^2
AB^2 = 3^2 - 4^2
AB^2 = 9 - 16
AB^2 = -7
Since AB^2 is negative, we know that there is no real solution for AB. This means that D cannot be on segment AB, and therefore, there is no distance between point D and point C in this scenario.
In summary, since AB^2 is negative, it tells us that there is no real solution for AB, and therefore, there is no distance from point D to point C in the given right triangle ABC.