1. Sine/Cosine/Tangent
Focus: Find out who is
sohacahtoa and why is the
spelling of his name so important?

2. sohcahtoa
• SOHCAHTOA was the chief of the
Trigonometric Tribe. He was a very wise
man and people would go to him to solve
their most pressing problems.
Legend has it that he is the grandson of
Sacajewea, for whom a famous park was
erected in SW Washington state in time for
Lewis and Clark to have a bath.

3. sohcahtoa
• SOHCAHTOA, a contemporary of Pythagorus,
worked on finding ways to solve lengths and
distances on right triangles.
• SOHCAHTOA is a famous dead mathematician,
but his name lives on in legendary brilliance, he
is still alive and working with roots.
• Spell his name correctly and you will certain
pass into the tribe of Trigonometry’s lore.

4. Right Triangles’ Sides
• Hypotenuse
• Adjacent side
• Opposite side
• The adjacent and opposite sides are
relative terms, compared to the location of
the angle in question.
• The hypotenuse is always across from the
right angle in a triangle.

5. Where they are found.
25°

6. Where the hypotenuse is found.
25°

7. Where the adjacent and opposite
sides are found.
25°
opposite
Adjacent means next to or attached. This will
be shown on the next slide.

8. Where the adjacent and opposite
sides are found.
25°
Adjacent side to the
25° angle.
Adjacent means next to or attached. The next slide
will show the relationships from the remaining angle.
Opposite
the 25°
angle.

9. Where the adjacent and opposite
sides are found relative to the third
angle..
65°
Adjacent
side
Adjacent means next to or attached. The hypotenuse is
still (always) across from the right angle.
Opposite the 65 degree angle.

10. Ratios
• Sine ratio:
– Opposite over
hypotenuse
• Cosine ratio:
– Adjacent over
hypotenuse
• Tangent ratio:
– Opposite over
Adjacent
9
12
15
Trigonometry is based on
the following relationships.
x°

11. Ratios
• Sine ratio:
– Opposite over
hypotenuse
9
12
15
x°
9
15

12. Ratios
• Sine ratio:
– Opposite over
hypotenuse
• Cosine ratio:
– Adjacent over
hypotenuse
9
12
9
12
15
x°
12
15

13. Ratios
• Sine ratio:
– Opposite over
hypotenuse
• Cosine ratio:
– Adjacent over
hypotenuse
• Tangent ratio:
– Opposite over
Adjacent
9
15
9
12
15
x°
9
12
12
15

14. Ratios
• Sine ratio:
– Opposite over
hypotenuse
• Cosine ratio:
– Adjacent over
hypotenuse
• Tangent ratio:
– Opposite over
Adjacent
9
12
15
Trigonometry charts are usually found at the back of math textbooks.
Is there one in your book on page 668?
x°
9
15
9
12
12
15 We can use these fractions as
division statements and compare
the resulting answers to determine
the angle’s measurement.

15. What is the missing angle
measurement?
.8000

9
15

9
12
12
15
.6000

.7500
