Right Triangle Trigonometry

Let’s Say We Have This Right Triangle 10 H 1.74 O 10° Ɵ A The reference angle is equal to 10° The hypotenuse is equal to 10 The ratio of the 𝒐𝒑𝒑𝒐𝒔𝒊𝒕𝒆 𝒔𝒊𝒅𝒆 𝒉𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔𝒆 = 𝟏.𝟕𝟒 𝟏𝟎 = 0.174 The opposite is equal to 1.74

Calculator Get it out of your bag

Calculator Zoom In Hit the ‘sin’ button Type in ’10’ Hit ‘enter’

Calculator sin (10) = 0.174

Let’s Say We Have This Right Triangle 10 H 3.42 O 20° Ɵ A The reference angle is equal to 20° The hypotenuse is equal to 10 The ratio of the 𝒐𝒑𝒑𝒐𝒔𝒊𝒕𝒆 𝒔𝒊𝒅𝒆 𝒉𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔𝒆 = 𝟑.𝟒𝟐 𝟏𝟎 = 0.342 The opposite is equal to 3.42

Calculator Zoom In Hit the ‘sin’ button Type in ’20’ Hit ‘enter’

Calculator sin (20) = 0.342

Let’s Say We Have This Right Triangle 10 H O 5 30° Ɵ A The reference angle is equal to 30° The hypotenuse is equal to 10 The ratio of the 𝒐𝒑𝒑𝒐𝒔𝒊𝒕𝒆 𝒔𝒊𝒅𝒆 𝒉𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔𝒆 = 𝟓 𝟏𝟎 = 0.5 The opposite is equal to 5

Calculator Zoom In Hit the ‘sin’ button Type in ’30’ Hit ‘enter’

Calculator sin (30) = 0.5

sin Ɵ = 𝐎𝐩𝐩𝐨𝐬𝐢𝐭𝐞 𝐇𝐲𝐩𝐨𝐭𝐞𝐧𝐮𝐬𝐞 What does this mean? The ratio of the opposite side length divided by the hypotenuse side length is equal to the sin of the reference angle. sin Ɵ = 𝐎𝐩𝐩𝐨𝐬𝐢𝐭𝐞 𝐇𝐲𝐩𝐨𝐭𝐞𝐧𝐮𝐬𝐞 H O sin Ɵ = 𝐎 𝐇 Ɵ A

Let’s Say We Have This Right Triangle 10 H O 10° Ɵ 9.85 A The reference angle is equal to 10° The hypotenuse is equal to 10 The ratio of the 𝒂𝒅𝒋𝒂𝒄𝒆𝒏𝒕 𝒔𝒊𝒅𝒆 𝒉𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔𝒆 = 𝟗.𝟖𝟓 𝟏𝟎 = 0.985 The adjacent is equal to 9.85

Calculator Zoom In Hit the ‘cos’ button Type in ’10’ Hit ‘enter’

Calculator cos (10) = 0.985

Let’s Say We Have This Right Triangle 10 H O 20° Ɵ 9.40 A The reference angle is equal to 20° The hypotenuse is equal to 10 The ratio of the 𝒂𝒅𝒋𝒂𝒄𝒆𝒏𝒕 𝒔𝒊𝒅𝒆 𝒉𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔𝒆 = 𝟗.𝟒𝟎 𝟏𝟎 = 0.940 The adjacent is equal to 9.40

Calculator Zoom In Hit the ‘cos’ button Type in ’20’ Hit ‘enter’

Calculator cos (20) = 0.940

Let’s Say We Have This Right Triangle 10 O 30° Ɵ 8.66 A The reference angle is equal to 30° The hypotenuse is equal to 10 The ratio of the 𝒂𝒅𝒋𝒂𝒄𝒆𝒏𝒕 𝒔𝒊𝒅𝒆 𝒉𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔𝒆 = 𝟖.𝟔𝟔 𝟏𝟎 = 0.866 The adjacent is equal to 8.66

Calculator Zoom In Hit the ‘cos’ button Type in ’30’ Hit ‘enter’

Calculator cos (30) = 0.866

cos Ɵ = 𝐀𝐝𝐣𝐚𝐜𝐞𝐧𝐭 𝐇𝐲𝐩𝐨𝐭𝐞𝐧𝐮𝐬𝐞 What does this mean? The ratio of the adjacent side length divided by the hypotenuse side length is equal to the cos of the reference angle. cos Ɵ = 𝐀𝐝𝐣𝐚𝐜𝐞𝐧𝐭 𝐇𝐲𝐩𝐨𝐭𝐞𝐧𝐮𝐬𝐞 H O cos Ɵ = 𝐀 𝐇 Ɵ A

Let’s Say We Have This Right Triangle 1.76 O 10° Ɵ 10 A The reference angle is equal to 10° The adjacent is equal to 10 The ratio of the 𝒐𝒑𝒑𝒐𝒔𝒊𝒕𝒆 𝒔𝒊𝒅𝒆 𝒂𝒅𝒋𝒂𝒄𝒆𝒏𝒕 𝒔𝒊𝒅𝒆 = 𝟏.𝟕𝟔 𝟏𝟎 = 0.176 The opposite is equal to 1.76

Calculator Zoom In Hit the ‘tan’ button Type in ’10’ Hit ‘enter’

Calculator tan (10) = 0.176

Let’s Say We Have This Right Triangle O 3.64 20° Ɵ A 10 The reference angle is equal to 20° The adjacent is equal to 10 The ratio of the 𝒐𝒑𝒑𝒐𝒔𝒊𝒕𝒆 𝒔𝒊𝒅𝒆 𝒂𝒅𝒋𝒂𝒄𝒆𝒏𝒕 𝒔𝒊𝒅𝒆 = 𝟑.𝟔𝟒 𝟏𝟎 = 0.364 The opposite is equal to 3.64

Calculator Zoom In Hit the ‘tan’ button Type in ’20’ Hit ‘enter’

Calculator tan (20) = 0.364

Let’s Say We Have This Right Triangle O 5.77 30° Ɵ A 10 The reference angle is equal to 30° The adjacent is equal to 10 The ratio of the 𝒐𝒑𝒑𝒐𝒔𝒊𝒕𝒆 𝒔𝒊𝒅𝒆 𝒂𝒅𝒋𝒂𝒄𝒆𝒏𝒕 𝒔𝒊𝒅𝒆 = 𝟓.𝟕𝟕 𝟏𝟎 = 0.577 The opposite is equal to 5.77

Calculator Zoom In Hit the ‘tan’ button Type in ’30’ Hit ‘enter’

Calculator tan (30) = 0.577

tan Ɵ = 𝐎𝐩𝐩𝐨𝐬𝐢𝐭𝐞 𝐀𝐝𝐣𝐚𝐜𝐞𝐧𝐭 What does this mean? The ratio of the opposite side length divided by the adjacent side length is equal to the tan of the reference angle. tan Ɵ = 𝐎𝐩𝐩𝐨𝐬𝐢𝐭𝐞 𝐀𝐝𝐣𝐚𝐜𝐞𝐧𝐭 H O tan Ɵ = 𝐎 𝐀 Ɵ A

Trigonometric Functions sin Ɵ = 𝐎 𝐇 cos Ɵ = 𝐀 𝐇 tan Ɵ = 𝐎 𝐀 SOH CAH TOA H O Ɵ A