In a right-angled triangle ABC with side lengths AB = 4, BC = 3, and AC = 5, the length of A'C' is 3.75 units. The measure of angle A' is 37 degrees.
In a right-angled triangle ABC, we have angle BAC = 37 degrees, ABC = 90 degrees, and ACB = 53 degrees.
Given that side AB = 4, side BC = 3, and side AC = 5, we can use the properties of similar triangles to find the length of A'C' and the measure of angle A'.
Using the property that the corresponding angles in similar triangles are equal, we can say that triangle ABC is similar to triangle A'C'B'.
Since the ratios of corresponding sides of similar triangles are equal, we have:
A'C' / AC = BC / AB
A'C' / 5 = 3 / 4
A'C' = (3/4) * 5 = 15/4 = 3.75
So, the length of A'C' is 3.75 units.
Since corresponding angles are equal in similar triangles, angle A' is also equal to angle BAC, which is 37 degrees.
The probable question may be:
In Right angled triangle ABC Angle BAC=37 degree, ABC=90 degree, ACB=53 degree, side AB=4, side BC=3,side AC=5
What is A'C', the length of bar AC after the dilation? what is the measure of angle A'?
A. A'C'=15 , measure angle A'=53 degree
A. A'C'=25 , measure angle A'=37 degree
A. A'C'=1 , measure angle A'=37 degree
A. A'C'=25 , measure angle A'=185 degree