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Question 1 of 5
Name the following sides with respect to angle θθ in the triangle below.
The sides can either be ABAB, ACAC or BCBC.
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We can easily identify the hypotenuse as it is simply the side opposite the right angle.
Therefore, the hypotenuse is side ACAC.
Next, the opposite side is exactly the side opposite the angle θθ.
Therefore, the opposite side is side BCBC.
Finally, the adjacent side is exactly the side next to the angle θθ, but not the hypotenuse.
Therefore, the adjacent side is side ABAB.
(i)(i) Opposite: BCBC
(ii)(ii) Adjacent: ABAB
(iii)(iii) Hypotenuse: ACAC
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Question 2 of 5
Find the following trigonometric ratios using the given triangle.
Write fractions in the format “a/b”
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Trigonometric Ratios (SOHCAHTOA) for Right Angled Triangles
First, label the values in the triangle.
opposite=5opposite=5
adjacent=12
hypotenuse=13
Now, solve each Trigonometric Ratio using the given formulas.
sinθ |
= |
oppositehypotenuse |
sin ratio |
|
|
= |
513 |
Plug in the values |
cosθ |
= |
adjacenthypotenuse |
cos ratio |
|
|
= |
1213 |
Plug in the values |
tanθ |
= |
oppositeadjacent |
tan ratio |
|
|
= |
512 |
Plug in the values |
(i) sinθ=513
(ii) cosθ=1213
(iii) tanθ=512
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Question 3 of 5
Find the following trigonometric ratios using the given triangle.
Write fractions in the format “a/b”
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Trigonometric Ratios (SOHCAHTOA) for Right Angled Triangles
First, label the values in the triangle.
opposite=15
adjacent=8
hypotenuse=17
Now, solve each Trigonometric Ratio using the given formulas.
sinθ |
= |
oppositehypotenuse |
sin ratio |
|
|
= |
1517 |
Plug in the values |
cosθ |
= |
adjacenthypotenuse |
cos ratio |
|
|
= |
817 |
Plug in the values |
tanθ |
= |
oppositeadjacent |
tan ratio |
|
|
= |
158 |
Plug in the values |
(i) sinθ=1517
(ii) cosθ=817
(iii) tanθ=158
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Question 4 of 5
Find the following trigonometric ratios using the given triangle.
Write fractions in the format “a/b”
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Trigonometric Ratios (SOHCAHTOA) for Right Angled Triangles
First, label the values in the triangle.
opposite=60
adjacent=11
hypotenuse=61
Now, solve each Trigonometric Ratio using the given formulas.
sinθ |
= |
oppositehypotenuse |
sin ratio |
|
|
= |
6061 |
Plug in the values |
cosθ |
= |
adjacenthypotenuse |
cos ratio |
|
|
= |
1161 |
Plug in the values |
tanθ |
= |
oppositeadjacent |
tan ratio |
|
|
= |
6011 |
Plug in the values |
(i) sinθ=6061
(ii) cosθ=1161
(iii) tanθ=6011
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Question 5 of 5
Find which angle in this triangle, A, B or C, has the following trigonometric ratios:
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Trigonometric Ratios (SOHCAHTOA) for Right Angled Triangles
Label the triangle according to each given trigonometric ratio to find the angles.
tanθ=oppositeadjacent=512
The angle opposite of 5 and adjacent to 12 is A
sinθ=oppositehypotenuse=1213
The angle opposite of 12 and has a hypotenuse of 13 is B
(i) tanθ=512:A
(ii) sinθ=1213:B