If the circumradius of triangle ABC is 10 cm and the area is 48 cm², what is the
Practice Questions
Q1
If the circumradius of triangle ABC is 10 cm and the area is 48 cm², what is the length of the side opposite to angle A?
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Questions & Step-by-Step Solutions
If the circumradius of triangle ABC is 10 cm and the area is 48 cm², what is the length of the side opposite to angle A?
Step 1: Understand the problem. We have a triangle ABC with a circumradius (R) of 10 cm and an area of 48 cm². We need to find the length of the side opposite to angle A, which we will call 'a'.
Step 2: Recall the formula that relates the circumradius (R), the sides of the triangle (a, b, c), and the area (Area): R = (abc) / (4 * Area).
Step 3: Rearrange the formula to solve for 'a': a = (4 * Area * R) / (bc).
Step 4: Substitute the known values into the formula: Area = 48 cm² and R = 10 cm. So, a = (4 * 48 * 10) / (b * c).
Step 6: Now we have a = 1920 / (b * c). To find the exact value of 'a', we need the values of sides 'b' and 'c'. Without those, we can only express 'a' in terms of 'b' and 'c'.
Circumradius and Area Relationship – Understanding the relationship between the circumradius (R), the sides of the triangle (a, b, c), and the area of the triangle.
Triangle Properties – Knowledge of how to apply the formula for the circumradius in relation to the sides of a triangle and its area.
