To find the unknown side length in a triangle, we can use the Law of Sines.
The Law of Sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is constant for all three sides of the triangle.
In this case, we have two angles, 20 and 30 degrees. Let's call the unknown side length "x."
We can set up the equation:
sin(20°) / x = sin(30°) / (opposite side)
Using a calculator, we can calculate the values of the two sines:
sin(20°) ≈ 0.3420
sin(30°) ≈ 0.5000
Plugging these values into the equation, we get:
0.3420 / x = 0.5000 / (opposite side)
Next, we rearrange the equation to solve for the opposite side:
(opposite side) = (0.5000 * x) / 0.3420
Now we can solve for the opposite side by substituting the known values:
(opposite side) ≈ (0.5000 * x) / 0.3420
Let's say x = 10. Plugging in this value:
(opposite side) ≈ (0.5000 * 10) / 0.3420
(opposite side) ≈ 14.6198
Therefore, the unknown side length, rounded to the nearest hundredth, is approximately 14.62.
Find the unknown side length in the given triangle. Round to the nearest hundredth.(1 point)
angles are 20 and 30
1 answer