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When it comes to finding the area of a triangle, one may think of the classic base times height formula. However, when dealing with oblique triangles (triangles without a right angle), we often use the sine rule area formula. This is especially handy when you know two sides of a triangle and the included angle between them.

In our scenario, the formula is simply:

• Area = \(0.5 \, \times \, a \, \times \, c \, \times \, \sin(B)\)

Here, "a" and "c" are the known side lengths, and "B" is the angle between sides "a" and "c". The sine function helps in determining the proportion of the respective height of the triangle in relation to these sides. This formula provides an efficient way to calculate the area without knowing every side or height separately.

Always remember: calculate the sine of angle "B" in radians, as we'll explore why next.

The sine rule is like magic for solving triangles, especially when you're dealing with angles and sides that don't play nice in a right triangle. It's about ratios. The sine rule states that the ratio of the length of a side of a triangle to the sine of the angle opposite it is constant for all three sides and angles in the triangle:

• \(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)

But in our exercise, we used a variation of it to find the area. It comes from the idea that the sine function links the angle nicely with the opposite sides and acts like a conversion factor in our area formula.

This rule comes in handy not just for calculating area but also for finding unknown sides or angles. Master this rule, and you’ll solve triangles with ease!

Degree to radian conversion is a nifty trick that simplifies working with angles in trigonometry. Most trigonometric functions in mathematical computations and calculators require angles in radians.

The conversion formula is quite straightforward:

• Radians = Degrees \(\times \frac{\pi}{180}\)

In the context of our problem, for angle \(B = 70^{\circ}\), converting it to radians makes it \(70 \times \frac{\pi}{180}\). This ensures your calculator knows exactly what you're talking about when you ask it to find \(\sin(70^{\circ})\).

Understanding how to toggle between degrees and radians will not only make solving triangles easier but also open up a wider world of understanding periodic functions, constellations, and rotational movements.