a right triangle's hypotenuse is 20 cm long. what is the length of the side opposite a 60 angle? give your answer to the nearest tenth of a centimeter.
A ) 40
B ) 18.5
C ) 20
D ) 17.3
To find the length of the side opposite a 60-degree angle in a right triangle, we will use the trigonometric function sine (sin).
The sine of an angle in a right triangle is defined as the length of the side opposite the angle divided by the length of the hypotenuse.
sin(60°) = opposite / hypotenuse
Since the hypotenuse is given as 20 cm, we can rewrite the equation as:
sin(60°) = opposite / 20
To solve for the length of the side opposite the 60-degree angle, we can rearrange the equation:
opposite = sin(60°) * 20
Using a calculator, we find that sin(60°) ≈ 0.866.
Therefore, the length of the side opposite the 60-degree angle is approximately:
opposite ≈ 0.866 * 20 ≈ 17.32 cm
Rounding to the nearest tenth of a centimeter gives us approximately 17.3 cm.
Therefore, the answer is D) 17.3.