One of the angles of a right triangle measures 30°, and the hypotenuse is 10 inches long. How long is the side opposite the 30° angle?
Well, if the hypotenuse is 10 inches long and one of the angles is 30°, then I guess the side opposite the 30° angle must be... long enough to reach from one end to the other! But if you want a more specific answer, the side opposite the 30° angle would be exactly 5 inches long, thanks to some good old trigonometry. So remember, when life gives you right triangles, find the side opposite and make it a 5-inch party!
To find the length of the side opposite the 30° angle in a right triangle, we can use trigonometric ratios. In this case, we can use the sine function.
The sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. Therefore, we can write the equation:
sin(30°) = opposite side length / hypotenuse length
Since we know that the hypotenuse is 10 inches long, we can substitute this value into the equation:
sin(30°) = opposite side length / 10 inches
Now, we can solve for the length of the side opposite the 30° angle by rearranging the equation:
opposite side length = sin(30°) * 10 inches
Using a calculator, we can find the value of sin(30°) to be 0.5. Therefore, the length of the side opposite the 30° angle is:
opposite side length = 0.5 * 10 inches = 5 inches
So, the length of the side opposite the 30° angle in the right triangle is 5 inches.
To find the length of the side opposite the 30° angle in a right triangle, we can use the trigonometric function sine. The sine of an angle is the ratio of the length of the side opposite to the length of the hypotenuse.
In this case, we know the angle is 30° and the hypotenuse is 10 inches long. Therefore, we can use the sine function to find the length of the opposite side.
sin(30°) = opposite/hypotenuse
We substitute the given values:
sin(30°) = opposite/10
opposite = sin(30°) * 10
Now we need to calculate the sine of 30°. To do this, we can look up the value on a trigonometric table or use a calculator with a built-in trigonometric function.
sin(30°) is equal to 0.5. Therefore:
opposite = 0.5 * 10
opposite = 5 inches
So, the length of the side opposite the 30° angle is 5 inches.
sin 30° = x/10
x = 10sin30° = 5
or
using the ratio of sides of the 30-60-90 triangle
x/1 = 2/10
x = 5