Useing sine rule
The sine rule states that for any triangle ABC, the ratio of the length of a side to the sine of its opposite angle is constant. Mathematically, it can be written as:
a/sin(A) = b/sin(B) = c/sin(C)
where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the measures of the angles opposite to those sides, respectively.
To use the sine rule, follow these steps:
1. Identify the sides and angles of the triangle: Label the sides of the triangle as a, b, and c, and the angles as A, B, and C.
2. Determine the known values: Identify the values you know or can measure. This requires at least one side and its opposite angle or two sides and their included angle.
3. Decide which equation to use: Depending on the values you have, determine which equation from the sine rule you need to utilize. For example, if you know side a and angle A, you can use the equation a/sin(A) = b/sin(B) = c/sin(C).
4. Substitute the values: Plug in the known values into the equation and solve for the unknown value. Rearrange the equation as needed to isolate the unknown value.
5. Simplify and calculate: Evaluate the equation to find the value of the unknown side or angle.
6. Repeat as necessary: Use the sine rule for any additional unknown values.
Remember that the sine rule applies for any triangle, not just right-angled triangles. It is especially useful when you don't have access to the lengths of all sides or all angles but need to find missing measurements in the triangle.