In a triangle ABC, angle C is 90⁰ and AB is 3cm. The length of side AC will be
We cannot determine the length of side AC with the given information.
Yes, something is missing.
Yes, you are right. To determine the length of side AC, we need additional information. We either need to know the length of side BC or the measure of an angle other than angle C. Then, we can use the Pythagorean theorem or trigonometric ratios to solve for the length of side AC.
To find the length of side AC in a right triangle ABC, where angle C is 90 degrees and AB is given as 3 cm, 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 lengths of the other two sides.
In this case, AC is the hypotenuse, and AB and BC are the other two sides. Let's assume that BC is the side adjacent to angle C.
Using the Pythagorean theorem, we have:
AC^2 = AB^2 + BC^2
Since AB is given as 3 cm, we can substitute this value into the equation:
AC^2 = (3 cm)^2 + BC^2
Simplifying, we have:
AC^2 = 9 cm^2 + BC^2
Since angle C is 90 degrees, we know that BC is the height of the triangle. Therefore, BC is the length of the side opposite to angle C.
In a right triangle, the length of the side opposite angle C is known as the altitude or height, and it can also be found using trigonometric ratios such as sine, cosine, or tangent. However, since we already have the length of the other side (AB = 3 cm), we can directly apply the Pythagorean theorem without using trigonometry.
Now, if we know the length of BC, we can substitute it into the equation and solve for AC. However, the information provided does not give us the length of BC.
Therefore, without knowing the length of BC or any other information about the triangle, we cannot determine the length of side AC.