Question

So I'm in an online class of geometry and one of the units is trig. but no matter how long i keep learning or trying to learn the notes and lesson i cant figure what it means. Or how to solve the triangle with anything other than Pythagorean's theorem which doesn't solve it or even help. And i try to look for a simpiler way to look at it but i cant find one.

Answer 1

Answer and explanation:

There are six main trigonometric ratios, namely: sine, cosine, tangent, cosecant, secant, cotangent.

Those ratios relate two sides of a right triangle and one angle.

Assume the following features and measures of a right triangle ABC

• right angle: B, measure β
• hypotenuse (opposite to angle B): length b

• angle C: measure γ
• vertical leg (opposite to angle C): length c

• horizontal leg (opposite to angle A): length a
• angle A: measure α

Then, the trigonometric ratios are:

• sine (α) = opposite leg / hypotenuse = a / b

• cosine (α) = adjacent leg / hypotenuse = c / b

• tangent (α) = opposite leg / adjacent leg = a / c

• cosecant (α) = 1 / sine (α) = b / a

• secant (α) = 1 / cosine (α) = b / c

• cotangent (α) = 1 / tangent (α) = c / b

Then, if you know one angle (other than the right one) of a right triangle, and any of the sides you can determine any of the other sides.

For instance, assume an angle to be 30º, and the lenght of the hypotenuse to measure 5 units.

• sine (30º) = opposite leg / 5 ⇒ opposite leg = 5 × sine (30º) = 2.5

• cosine (30º) = adjacent leg / 5 ⇒ adjacent leg = 5 × cosine (30º) = 4.3

Thus, you have solved for the two unknown sides of the triangle. The three sides are 2.5, 4.3, and 5.