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Day 3: Finding Unknown
Sides and Angles
Unit 8: Trigonometry
Learning Goals

To be able to find unknown sides and angles of a right
triangle
Remember… Primary Trig Ratios
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
= sin 𝑥
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡

ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
= cos 𝑥


𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
= tan 𝑥
To solve for an unknown side:
1.
Label the sides opp, adj, and hyp using the given
angle as your reference angle
2.
Decide which primary trig function to use based on
the given side and the required side
3.
Substitute in known values
4.
Solve for the unknown
Solve for the unknown.
a)
sin 57 =
𝑦
15
adjacent
opposite
𝑦 = 15 sin 57
𝑦 = 12.58
hypotenuse
To solve for an unknown angle:
1.
Label the sides opp, adj, and hyp using the required
angle as your reference angle
2.
Decide which primary trig function to use based on
the given sides
3.
Substitute in known values
4.
Solve for the unknown
Solve for the unknown.
b)
cos 𝑥 =
14.3
19
𝑥 = cos −1
hypotenuse
14.3
19
adjacent
𝑥 = 41°
opposite
Key Points

ONLY to be used with right angle triangles

Make sure calculator is in degree mode

Use sin, cos or tan button when looking for an unknown
side

Use the inverse version of sin, cos and tan
(sin−1 𝑥 , cos −1 𝑥 , tan−1 𝑥) when you are looking for an
unknown angle

“Solve the triangle” means find ALL missing side AND
angle values
Success Criteria

I CAN use primary trigonometric
ratios to find unknown sides and
angles of a right triangle
To Do…
 Two
questions
 Worksheet
 Check
the website daily for
updates, missed notes, assignment
solutions
 www.mrsmccrum.weebly.com