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Right Triangle Trigonometry
Unit 4 Lesson 1
RIGHT TRIANGLE TRIGONOMETRY
Students will be able to:
Use the right triangle trigonometry for finding the unknowns in a right angled triangle
Key Vocabulary:
β’ Right Triangle Trigonometry
β’ Trigonometric Ratios
β’ Pythagorean Theorem
Right Triangle Trigonometry
Right angle trigonometry is the trigonometry of a right-angled triangle.
A right-angled triangle is a triangle in which one angle is 90 degrees.
RIGHT TRIANGLE TRIGONOMETRY
Properties of a Right Angled Triangle
β’ A hypotenuse is the line segment opposite to the right-angle.
β’ An opposite is the line segment opposite to the angle Ο΄.
β’ An adjacent is the line segment next to the angle Ο΄.
RIGHT TRIANGLE TRIGONOMETRY
Trigonometric Ratios
There are total 6 trigonometric ratios for a right angled triangle.
1. Sine
2. Cosine
πππ π½ = ππππππππ
ππππππππππ
πππ π½ = ππ ππππππ
ππππππππππ
RIGHT TRIANGLE TRIGONOMETRY
3. Tangent
4. Cosecant
πππ π½ = ππππππππ
ππ ππππππ
πππππ π½ = ππππππππππ
ππππππππ=
π
πππ(π½)
RIGHT TRIANGLE TRIGONOMETRY
5. Secant
6. Cotangent
πππ π½ = ππππππππππ
ππ ππππππ=
π
πππ(π½)
πππ π½ = ππ ππππππ
ππππππππ=
π
πππ(π½)
RIGHT TRIANGLE TRIGONOMETRY
Problem 1: Write the trigonometric ratios for the angle πͺ in the triangle shown.
RIGHT TRIANGLE TRIGONOMETRY
Problem 1: Write the trigonometric ratios for the angle πͺ in the triangle shown.
πππ πͺ =
ππ
ππ=
π
ππ
πππ πͺ =ππ
ππ=
ππ
ππ
πππ πͺ =ππ
ππ=
π
ππ
πππππ πͺ =ππ
ππ=
ππ
π
πππ πͺ =ππ
ππ=
ππ
ππ
πππ πͺ =ππ
ππ=
ππ
π
RIGHT TRIANGLE TRIGONOMETRY
Problem 2: Find the value of π. Round to the nearest tenth.
RIGHT TRIANGLE TRIGONOMETRY
Problem 2: Find the value of π. Round to the nearest tenth.
ππππ½ = πππ
πππ
πππππΒ° =π
ππ
π = ππ Γ πππππΒ° π = π. π
RIGHT TRIANGLE TRIGONOMETRY
Pythagorean Theorem
In a right-triangle, the sum of the squares of the lengths of adjacent and opposite is equal to the square of the length of hypotenuse.
Where,
π = π―πππππππππ
π = πΆπππππππ
π = π¨π ππππππ
ππ = ππ + ππ
RIGHT TRIANGLE TRIGONOMETRY
Problem 3: Find the unknown length π in the right triangle shown.
RIGHT TRIANGLE TRIGONOMETRY
Problem 3: Find the unknown length π in the right triangle shown.
By Pythagorean theorem,
ππ = ππ + ππ πππ = ππ + πππ ππ = πππ β πππ
ππ = ππ π = π
RIGHT TRIANGLE TRIGONOMETRY