Download Equation Chapter 1 Section 1TRIGONOMETRY MUST be a right

TRIGONOMETRY
1. MUST be a right-angled triangle.
2. Identify all sides.
Opposite
Hypotenuse
x0
Adjacent
Hypotenuse: The largest side. Not next to right angle.
Opposite:
Side does not touch named angle.
Adjacent:
Only side left. Next to named angle.
To find a side:
Need to know one other side and an angle.
1.
2.
3.
4.
5.
6.
Label the known side A, O or H.
Label the side you are trying to find A, O or H.
Write the word SOHCAHTOA.
Tick the two labelled sides.
Which ratio has two ticks?
Use this ratio.
x
15 cm
550
Example:
Find the value of x
1. Label the side you know and the side you are trying to find
O
H
550
2. SOHCAHTOA
3.
Notice that the S has two marked sides and the C and T only one. This means
that ratio to use is Sine.
O
H
Sin 550 =
Sin 550 =
x
15
15 x Sin 550 = x
15 x 0.819152044 = x
12.29 = x
Note that this has been rounded to 2 decimal places. Don’t forget units.
4.
Answer is x = 12.29 cm.
To find an angle:
Need to know two sides.
20 cm
Find the value of x
1. Label the side you know and the side you are trying to find
x0
16 cm
2. SOHCAHTOA
3. This time the required ratio is Cosine.
4.
cos x0 =
cos x0 =
A
H
16
20
cos x0 = 0.8
(Using Second Function)
x0 = cos -1 0.8
x0 = 36.90
Answer has been rounded to one decimal place.