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?
Practice Questions
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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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Using the formula R = (abc)/(4 * Area), we can find the side opposite to angle A. Let a = side opposite to A. Then, a = (4 * Area * R) / (bc) = (4 * 48 * 10) / (b * c).
Questions & Step-by-step Solutions
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Q
Q: 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?
Solution: Using the formula R = (abc)/(4 * Area), we can find the side opposite to angle A. Let a = side opposite to A. Then, a = (4 * Area * R) / (bc) = (4 * 48 * 10) / (b * c).
Steps: 6
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'.
