The three angles of a triangle are 105°,25°,50° .
In what ratios are the sides?
Sin A/a = sin B/b = sin C/c
What do you do next?
To determine the ratios of the sides of a triangle, we can use the Law of Sines or the Law of Cosines.
In this case, let's use the Law of Sines, which states that the ratio of a side of a triangle to the sine of its opposite angle is the same for all three sides.
Let's label the angles of the triangle as A, B, and C, and the sides opposite to them as a, b, and c respectively.
The given angles are A = 105°, B = 25°, and C = 50°.
We can select any two angles and their corresponding sides to calculate the ratios. Let's take angles A and B, along with sides a and b.
Using the Law of Sines, we have:
sin(A)/a = sin(B)/b
Substituting the given values:
sin(105°)/a = sin(25°)/b
Now, we need to find the value of sin(105°). Since sin(105°) is not a common angle measure, we can use the identity: sin(180° - x) = sin(x).
So, sin(105°) = sin(180° - 105°) = sin(75°).
Substituting back into the equation:
sin(75°)/a = sin(25°)/b
Since sin(75°) is still a trigonometric function, we cannot find its exact value. However, we can use a calculator to approximate it.
Now, we can rearrange the equation to solve for the ratio of sides:
a/b = sin(75°)/sin(25°)
Using a calculator, we find:
a/b ≈ 3.73205
Therefore, the ratio of the sides a:b in the given triangle is approximately 3.73205.
Note that this ratio is specific to sides a and b, so if you want to find the ratios for other combinations of sides, you will need to use the appropriate angles and apply the Law of Sines again.