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In a right triangle, one angle is 3030 degrees and the hypotenuse is 1010 meters. Find the length of the opposite side. (Specify answer in sine, cosine, or tangent form)

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Q. In a right triangle, one angle is 3030 degrees and the hypotenuse is 1010 meters. Find the length of the opposite side. (Specify answer in sine, cosine, or tangent form)
  1. Use Sine Function: In a right triangle, the sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse. So, we use the sine function for the 3030-degree angle.
  2. Calculate sin⁡(30∘)\sin(30^\circ): sin⁡(30∘)=Opposite SideHypotenuse\sin(30^\circ) = \frac{\text{Opposite Side}}{\text{Hypotenuse}}
  3. Plug in Hypotenuse: We know the hypotenuse is 1010 meters, so plug that into the equation.\newlinesin⁡(30∘)=Opposite Side10\sin(30^\circ) = \frac{\text{Opposite Side}}{10}
  4. Substitute Known Value: sin⁡(30∘)\sin(30^\circ) is a known value, which is 12\frac{1}{2}.12=Opposite Side10\frac{1}{2} = \frac{\text{Opposite Side}}{10}
  5. Solve for Opposite Side: Now, solve for the Opposite Side by multiplying both sides by 1010.10×(12)=Opposite Side10 \times \left(\frac{1}{2}\right) = \text{Opposite Side}
  6. Final Result: Opposite Side = 10×(12)10 \times \left(\frac{1}{2}\right)\newlineOpposite Side = 55 meters

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