Description
These are the four steps we need to follow:
- Step 1 Find which two sides we know – out of Opposite, Adjacent and Hypotenuse.
- Step 2 Use SOHCAHTOA to decide which one of Sine, Cosine or Tangent to use in this question.
- Step 3 For Sine calculate Opposite/Hypotenuse, for Cosine calculate Adjacent/Hypotenuse or for Tangent calculate Opposite/Adjacent.
- Step 4 Find the angle from your calculator, using one of sin-1, cos-1 or tan-1
Example
Find the size of angle a0
- Step 1 The two sides we know are Adjacent (6,750) and Hypotenuse (8,100).
- Step 2 SOHCAHTOA tells us we must use Cosine.
- Step 3 Calculate Adjacent / Hypotenuse = 6,750/8,100 = 0.8333
- Step 4 Find the angle from your calculator using cos-1 of 0.8333:
cos a0 = 6,750/8,100 = 0.8333
cos-1 of 0.8333 = 33.60 (to 1 decimal place)
Example #1
Find the missing angle when you are given the following dimensions.
BC = 3; AC = 16; AB = 8, Cos ? = 3/16
Explanation
The missing value is x than Cos 3 / 16
Cos x = 0.2
x = Cos-1 0.2
x = 78.5
Answer = 78.50
Practice Problem #1:
Find the missing angle:
BC = 10 ; AC = 18 ; AB = 7, Sin__?__ = 7 / 18
Explanation #1
The missing value is x than Sin 7 / 18
Sin x = 0.4
x = Sin-1 0.4
x = 23.60
Answer = 23.60
Practice Problem #2)
Find the missing angle:
BC = 24 ; AC = 13 ; AB = 4, tan_?___ = 13 / 24
Explanation #2
The missing value is x than tan 13 / 24
tan x = 0.5
x = tan-1 0.5
x = 26.60
Answer = 26.60
Practice Problem #3)
Find the missing angle:
BC = 18 ; AC = 33 ; AB = 15, Cos__?__ = 18 / 33
Explanation #3
The missing value is x than Cos 18 / 33
Cos x = 0.5
x = Cos-1 0.5
x = 600
Answer = 600
Review
Directions: Find the missing angle in each of the following problems.
1. QR = 36 ; PR = 45 ; PQ = 21, Sin __?___ = 21 / 45
2. QR = 16 ; PR = 2 ; PQ = 8, tan __?__ = 8 / 16
3. QR = 15 ; PR = 28 ; PQ = 15, Cos __?__ = 15 / 28
4. QR = 47 ; PR = 64 ; PQ = 38, tan __?__ = 38 / 47
5. QR = 4 ; PR = 17 ; PQ = 12, Sin __?___ = 12 / 17
6. QR = 36 ; PR = 59 ; PQ = 20, Cos __?___ = 36 / 59
7. QR = 82 ; PR = 63 ; PQ = 29, tan __?__ = 29 / 82
8. QR = 10 ; PR = 28 ; PQ = 8, Sin __?___ = 8 / 28
9. QR = 51 ; PR = 42 ; PQ = 9, tan __?__ = 9 / 51
10. QR = 16 ; PR = 20 ; PQ = 17, Cos __?___ = 16 / 20
11. QR = 12 ; PR = 84 ; PQ = 60, Sin __?_ = 60 / 84
12. QR = 19 ; PR = 32 ; PQ = 45, Cos __? = 19 / 32
13. QR = 76 ; PR = 27 ; PQ = 64, tan __ ?_ = 64 / 76
14. QR = 26 ; PR = 48 ; PQ = 37, Cos __?_ = 37 / 48
15. QR = 19 ; PR = 66 ; PQ = 23, Cos __?__= 23 / 66
