Download Solve for the unknown: Section 9-1: Solving Right Triangles

Solve for the unknown:
1)
2)
0.65 =
12
𝑥
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.
Labeling format
B
UPPER CASE
VERTICES
a
c
lower case
sides
A
b
C
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.
B
=
Using tan 28⁰:
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
𝑡𝑎𝑛𝜃 =
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
Using cot 28⁰:
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
𝑐𝑜𝑠𝜃 =
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
40
𝑡𝑎𝑛28° =
𝑏
𝑏
𝑐𝑜𝑠28° =
40
40
≈ 75.2
tan 28⁰
40𝑐𝑜𝑠28° ≈ 75.2
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
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