Right Triangles and SOHCAHTOA
There are two types of Trigonometry :
1. Right Triangle Trigonometry
2. Unit Circle Trigonometry
Let's look at the difference between these two trigs.
Unit Circle Trigonometry
~ Used to graph sine and cosine functions.
~ We can rotate the angle around its circumference and plot its points on an x- and y-axis.
~ We would be using y for sine and x for cosine, giving us a different graph.
~ Angles are from 0 degrees to 360 degrees or 0π to 2π radians.
~ The trig functions are sin x, cos x, tan x, and reciprocal functions... sec x, csc x, cot x.
Right Triangle Trigonometry
~ Used to find the height of a tree.
~ Used to determine how far away we are from the moon.
~ Used to find angles of elevations and depressions.,
~ Angles used are between 0 degrees and 90 degrees.
~ Angles are in degrees NOT radians.
~ The common trig functions used are sin, cos, and tan.
~ The following memory device can be used when working with Right Triangle Trig.
SOH CAH TOA
Sine: sin θ =opposite/hypotenuse
Cosine: cos θ =adjacent/hypotenuse
Tangent : tan θ = opposite/adjacent
Example 1
A forester, 175 feet from the base of a redwood tree, observes that the angle between the ground and the top of the tree is 55 degrees.
Estimate the height of the tree. Round your answer to the nearest tenth.
Given
~ the distance between the forester and the tree is 175 (adjacent side)
~ the angle from the ground to the top of the tree is 55º (angle)
Looking for
the height of the tree... x (opposite the angle)
Work (Right --->
Example 2
A ladder, 500 cm long, leans against a building.
The angle between the ground and the ladder is 57 degrees.
How far from the wall is the bottom of the ladder?
Round the answer to the nearest tenth.
Given
~ the length of the ladder is 500 (hypotenuse)
~ the angle between the ground and the ladder (the angle)
Looking for
the distance from the wall to the bottom of the ladder (x)
Work (Right --->