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