An isosceles triangle ABC has its vertices on a circle. If /AB/=13 cm, /BC/=13 cm and /AC/=10 cm, calculate the height BM of the triangle
12 cm
correct.
5^2 + 12^2 = 13^2
Not sure why mention was even made of the circle.
To find the height of the isosceles triangle, we need to draw an altitude from vertex B to the base AC. Let's label the point where the altitude intersects the base as point M.
First, let's find the length of BM using the Pythagorean theorem. The Pythagorean theorem states that in a right-angled 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 triangle ABM, AB is the hypotenuse, and BM and AM are the other two sides. Since triangle ABM is a right triangle, we can use the Pythagorean theorem to find BM.
Using the Pythagorean theorem:
BM^2 + AM^2 = AB^2
Now, let's substitute the given values:
BM^2 + 10^2 = 13^2
Simplifying the equation:
BM^2 + 100 = 169
Subtracting 100 from both sides:
BM^2 = 69
Taking the square root of both sides:
BM = √69 cm
So, the height of the isosceles triangle, BM, is approximately √69 cm.