Solve for the unknown:

1) 0.65 =12

𝑥

2) 0.32 =𝑥

4

Section 9-1: Solving Right Triangles

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

right triangle.

Types of triangles

Scalene

Isosceles

Equilateral

Right

Types of triangles

Scalene

Isosceles

Equilateral

Right

Types of angle

Right

Acute

Obtuse

vocabulary

Vertex… vertices

Pythagorean 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 case

sides

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 or cot 28⁰.

Using tan 28⁰:

𝑡𝑎𝑛𝜃 =𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒

𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡

Using cot 28⁰:

40

tan 28⁰≈ 75.2

B

=

𝑡𝑎𝑛28° =40

𝑏

𝑐𝑜𝑠𝜃 =𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡

ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

40𝑐𝑜𝑠28° ≈ 75.2

𝑐𝑜𝑠28° =𝑏

40

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

SEE ATTACHED WORKSHEET FOR PRACTICE PROBLEMS