A series of free, online High School Geometry Video Lessons and solutions. In these lessons, we will learn
The following diagram shows the trigonometric ratios using SOHCAHTOA. Scroll down the page if you need more examples and solutions on how to use the trigonometric ratios.
Right triangles have ratios to represent the angles formed by the hypotenuse and its legs. Sine ratios, along with cosine and tangent ratios, are ratios of the lengths of two sides of the triangle. Sine ratios in particular are the ratios of the length of the side opposite the angle they represent over the hypotenuse. Sine ratios are useful in trigonometry when dealing with triangles and circles.
How to define the sine ratio and identify the sine of an angle in a right triangle?
Identify the hypotenuse of a right triangle.
sin θ = opposite/hypotenuse
A word problem involving the trigonometric ratio of sine to calculate the height of a pole
A 55 ft wire connects a point on the ground to the top of a pole. The cable makes an angle of 60° with the ground. Find the height of the pole to the nearest foot.
Right triangles have ratios that are used to represent their base angles. Cosine ratios, along with sine and tangent ratios, are ratios of two different sides of a right triangle.Cosine ratios are specifically the ratio of the side adjacent to the represented base angle over the hypotenuse. In order to find the measure of the angle, we must understand inverse trigonometric functions.
How to use the Cosine formula (the CAH Formula) to find missing sides or angles?
Cosine θ = adjacent/hypotenuse
Find the missing side or angle
a) cos 30° = x/2
b) cos 37° = 4.2/x
c) cos θ = 63/80
How to apply the Sine and Cosine Ratios?
Sine, cosine are trigonometric ratios for the acute angles and involve the length of a leg and the hypotenuse of a right triangle.
Angle of elevation - When looking up at an object, the angle your line of sight makes with a horizontal line is called the angle of elevation.
Angle of depression - When looking down at an object, the angle your line of sight makes with a horizontal line is called the angle of depression.
Right triangles have ratios that are used to represent their base angles. Tangent ratios, along with cosine and sine ratios, are ratios of two different sides of a right triangle. Tangent ratios are the ratio of the side opposite to the side adjacent the angle they represent. In order to find the measure of the angle itself, one must understand inverse trigonometric functions.
How to use the Tangent formula (the TOA Formula)?
Tangent θ = opposite/adjacent
Find the missing side or angle
a) tan 28° = x/40
b) tan 41° = 1.9/x
c) tan θ = 11/8
Applications of Trigonometric Ratios (Word Problems Involving Tangent, Sine and Cosine)
Once we understand the trigonometric functions sine, cosine, and tangent, we are ready to learn how to use inverse trigonometric functions to find the measure of the angle the function represents. Inverse trigonometric functions, found on any standard scientific or graphing calculator, are a vital part of trigonometry and will be encountered often in Calculus.
How to use inverse trigonometric functions to find an angle with a given trigonometric value and how to use inverse trigonometric functions to solve a right triangle?
Use the calculator to find an angle θ in the interval [0, 90] that satisfies the equation.
How to use inverse trig to find a missing angle?
Inverse trig functions are used to find missing angles rather than missing sides.
Find missing Angles - Using Inverse Sine, Cosine, Tangent
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