1. Grade 10 Academic (MPM2D) Unit 5: Trigonometry Solving Right Triangles
Mr. Choi
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2. Trigonometry is a branch of mathematics that studies the relationship between the measures of the angles and the lengths of the sides in triangles.
Solving Right Triangles
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3. Notation: In any triangle, the vertices are named using capital letters as in the given example. The lengths of the sides are named using lower case letters that match the opposite vertex.
Solving Right Triangles
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4. Sine (Sin), COSINE (Cos), TANGENT (Tan):
Opposite side
Adjacent side
Hypotenuse side
Solving Right Triangles
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5. Example 1: In the diagrams below, fill in the missing information.C K q d e T
Recall In any triangle, the vertices are named using capital letters as in the given example. The lengths of the sides are named using lower case letters that match the opposite vertex.
Solving Right Triangles
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6. Solving Right Triangles To solve a right triangle means to find all the unknown sides and unknown angles. It requires that you find the “missing” three pieces of information. As with congruent triangles, if you are given the proper three pieces of information you will draw a unique triangle. The three cases are: Case 1. SIDE-SIDE-SIDE Triangle Case 2. SIDE-ANGLE-SIDE Triangle Case 3. ANGLE-SIDE-ANGLE Triangle   The strategy to solve a right triangle will require: 1. The Pythagorean Theorem 2. The Sum of the Angles in a Triangle Theorem 3. Trigonometry
Solving Right Triangles
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7. Example 2: Solve the triangle
Example 2: Solve the triangle. (Nearest degree for angles & 1 decimal place for sides)
SOHCAHTOA c
For: Angle A
Given:
Adjacent & Hypotenuse
COSINE a b
For: Angle C
For: Angle C
Given:
Opposite & Hypotenuse OR
SINE
Solving Right Triangles
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8. Example 3: i) Draw the following right triangles
Example 3: i) Draw the following right triangles. Label all given information. ii) Solve the triangle. (Nearest degree for angles & 1 decimal place for sides) a) if
SOHCAHTOA
For: Angle J
Given:
Opposite & Adjacent
TANGENT g
j = 4
h = 10
For: Angle H
Given:
For: Angle H
Opposite & Adjacent OR
TANGENT
Solving Right Triangles
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9. Example 3: i) Draw the following right triangles
Example 3: i) Draw the following right triangles. Label all given information. ii) Solve the triangle. (Nearest degree for angles & 1 decimal place for sides) b) if
SOHCAHTOA
For: Side p
Use:
For: Angle P
Opposite & Hypotenuse
SINE
r = 12 p
35o q
For: Side q
Use:
Adjacent & Hypotenuse
COSINE OR
Solving Right Triangles
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10. Example 4: Isosceles Right Triangle (Special Angle  45o) Given an isosceles right triangle below, determine the hypotenuse m in exact radical form. Determine the value in exact radical form for the given trigonometric angles.
SOHCAHTOA
Solving Right Triangles
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11. Example 5: Equilateral Triangle (Special Angles  30o & 60o) Given an equilateral triangle below, bisect the triangle into half and find h in exact radical form. Determine the value in exact radical form for the given trigonometric angles.
SOHCAHTOA
Solving Right Triangles
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12. Example 6: Special Angles  30o , 45o & 60o) Copy the results from examples 4 & 5 and complete the table in exact radical form
30o
45o
60o
Sin
Cos
Tan
Solving Right Triangles
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13. Homework
Work sheet: Solving Right Triangles Text: P. 497 #8, 10, 17, 24, 26 Check the website for updates
Solving Right Triangles
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14. End of lesson Solving Right Triangles
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