Solve for the unknown:

Answers:1) x=18.46 2) x=1.28

Section 9-1: Solving Right Triangles

Objective: To use trigonometry to find unknown sides or angles of a

right triangle.Learn and remember triangle and

angle vocabulary

Types of triangles

ScaleneIsoscelesEquilateralRight

Types of triangles

Scalene Isosceles Equilateral Right

Types of angle

RightAcuteObtuse

vocabulary

Vertex… verticesPythagorean theorem

Hypotenuse

These are the general formulas you will need in order to find any unknown angle or side in a right triangle.

A

B

C

c

b

a

UPPER CASE VERTICES

lower casesides

Labeling format

To Solve a triangle

To solve a triangle means to find the value of ALL angles and sides.

Example:

Solve the triangle below:

Solution:To find the value of b, use either tan 28⁰

Using tan 28 :⁰

𝑡𝑎𝑛𝜃=𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡

Using sin 28 to find C ⁰

40tan 28⁰

≈75.2B=

𝑡𝑎𝑛28 °=40𝑏

sin

40𝑠𝑖𝑛28

≈85.20

sin

Example: continued

solutions:

B=62o

b=75.2c=85.2

Angles of Elevation and Depression

The angle of elevation of an object as seen by an observer is the angle between the horizontal and the line from the object to the observer's eye (the line of sight).

Angles of Elevation and Depression

If the object is below the level of the observer, then the angle between the horizontal and the observer's line of sight is called the angle of depression.

Parallel lines – equal angles

A

A

A

A

B

B

B

B

Alternate interior angles are congruent

A

A

A

A

B

B

BB

Vertical angles are congruent

A

A

A

A

B

B

B

B

Corresponding angles are congruent

A

A

A

A

B

B

BB

Parallel lines – supplementary angles

A

A

A

A

B

B

B

B

The sum of A + B is 180

A

A

A

A

B

B

B

B

Linear pairs are supplementary

A

A

A

A

B

B

B

B

Same-side-interior angles are supplementary

A

A

A

A

B

B

B

B

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