a triangles base measures 12 cm, one angle measures 90 degrees, another angle measures 35 degrees, what is the length of the shortest side?
To find the length of the shortest side, we need to use the sine function. Since we know the measure of one angle, we can use the sine of that angle to find the length of the corresponding side.
Let's label the sides of the triangle: the side opposite the 90-degree angle is the hypotenuse (H), the base is the side adjacent to the 35-degree angle (B), and the shortest side is the side opposite the 35-degree angle (S).
We know that sin(35 degrees) = S/H, where H = 12 cm.
Rearranging the equation, we have S = H * sin(35 degrees).
Substituting the values, we have S = 12 cm * sin(35 degrees).
Using a calculator, we find that sin(35 degrees) ≈ 0.574.
Thus, the length of the shortest side (S) ≈ 12 cm * 0.574 ≈ 6.89 cm.
Therefore, the length of the shortest side is approximately 6.89 cm.