right triangle trigonometry find the value of trigonometric functions of acute angles use the...
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Right Triangle Trigonometry
Find the value of trigonometric functions of acute anglesUse the complementary angle theorem
Solve right trianglesSolve applied
Right Triangles
A triangle in which one angle is a right angle is called a right triangle
OppositeSide
Hypotenuse
Adjacent Side
Pythagorean Theorem
a2 + b2 = c2
cb
a
Trigonometric Functions
a
b
adjacent
opposite
c
a
hypotenuse
adjacent
c
b
hypotenuse
opposite
tan
cos
sin
b
a
opposite
adjacent
a
c
adjacent
hypotenuse
b
c
opposite
hypotenuse
cot
sec
csc
Complementary Angles:
Co-functions of complementary angles are equal
sin 30° = cos 60°tan 40° = cot 50°sec 80° = csc 10°
Solving Right triangles
To solve a right triangle means to find the missing lengths of its sides and the measurements of its angles
Solving a right triangle
Use the figure. If b=2 and α = 40°, find a, c and β.
c
a
2
40°
Finding the width of a river
A surveyor can measure the width of a river by setting up a transit at a point C on one side of the river and taking a sighting of a point A on the other side. After turning through an angle of 90° at C, the surveyor walks a distance of 200 meters to point B. Using the transit at B, the angle β is measured and found to be 20°. What is the width of the river rounded to the nearest meter?
Work and Diagram
Finding the inclination of a mountain trail
A straight trail leads from the Alpine Hotel, elevation 8000 ft, to a scenic overlook , elevation 11,100 feet. The length of the trail 14,100 feet. What is the inclination (grade) of the trail? That is what is the angle β
Angle of elevation and depression
Vertical heights can sometimes be measured using either the angle of elevation or the angle of depression.
Angle of elevation
Angle of depression
Classwork and Homework
Page 491 examples 9-13, 29-31, 50-56