The length of side AC is 20 cm. Supporting Details: 1. Identify the knowns and unknowns: We have a right-angled triangle ABC, with the right angle at B. Angle C = 30°; The side opposite to angle C (AB) = 10 cm. We need to find the length of the hypotenuse (AC). 2. Choose the appropriate trigonometric ratio: The sine function relates the opposite side, the hypotenuse, and the angle: sin(angle) = Opposite / Hypotenuse 3. Set up the equation: sin(C) = AB / AC; sin(30°) = 10 / AC 4. Solve for AC: We know that sin(30°) = 1/2. So, 1/2 = 10 / AC To solve for AC, cross-multiply: 1 * AC = 2 × 10; AC = 20 cm

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September 3, 2026Mathematics

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Answer

The length of side AC is 20 cm.

Step-by-step solution

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Supporting Details:

Identify the knowns and unknowns
- We have a right-angled triangle ABC, with the right angle at B.
- Angle C = 30°
- The side opposite to angle C (AB) = 10 cm.
- We need to find the length of the hypotenuse (AC).
Choose the appropriate trigonometric ratio
The sine function relates the opposite side, the hypotenuse, and the angle:
sin(angle) = Opposite / Hypotenuse
Set up the equation
sin(C) = AB / AC
sin(30°) = 10 / AC
Solve for AC
We know that sin(30°) = 1/2.
So, 1/2 = 10 / AC

To solve for AC, cross-multiply:
1 * AC = 2 * 10
AC = 20 cm

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Answer

Step-by-step solution

Identify the knowns and unknowns

Choose the appropriate trigonometric ratio

Set up the equation

Solve for AC

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