What are the three trig functions?

Question

b. What are the ratios of a 30-60-90 right triangle?
c. What are the ratios of a 45-45-90 right triangle?
d. How do you use trig to find the area of a triangle using trig?

Answer 1

The three trigonometric functions are sine (sin), cosine (cos), and tangent (tan).

b. In a 30-60-90 right triangle, the ratios of the sides are:

- The ratio of the length of the side opposite the 30-degree angle to the length of the hypotenuse is 1:2√3.
- The ratio of the length of the side opposite the 60-degree angle to the length of the hypotenuse is √3:2.
- The ratio of the length of the shorter leg (opposite the 30-degree angle) to the length of the longer leg (opposite the 60-degree angle) is 1:√3.

c. In a 45-45-90 right triangle, the ratio of the sides are:

- The sides of the triangle are congruent.
- The ratio of the length of both legs to the length of the hypotenuse is 1:√2.

d. To find the area of a triangle using trigonometry, you can use the formula:

Area = 0.5 * a * b * sin(C)

Where a and b are the lengths of two sides of the triangle and C is the angle between those sides. This formula is derived from the formula for the area of a triangle, which is 0.5 * base * height. In trigonometry, the height is represented by the side opposite to the angle C, and the base can be determined using the trigonometric functions.