Trigonometry – Tangent – Angles – Demonstration This resource provides animated demonstrations of the mathematical method. Check animations and delete slides not needed for your class.

θ Hypotenuse Opposite Adjacent A right-angled triangle has 4 parts. θ = Theta is either angle. Hypotenuse Opposite θ Adjacent Hypotenuse – always opposite the right-angle & always longest. Opposite – always opposite θ. Adjacent – next to θ.

TOA 𝑥 (O) 12 cm 9 cm (A) 𝑇𝑎𝑛 θ= 𝑂𝑝𝑝 𝐴𝑑𝑗 O A 𝑇𝑎𝑛 θ= 𝑂 𝐴 𝑇𝑎𝑛 𝑥= 12 9 Label the sides. Write the formula. Substitute & calculate. 𝑇𝑎𝑛 θ= 𝑂𝑝𝑝 𝐴𝑑𝑗 Find the value of 𝑥 to 2dp. O Tan θ A (O) We want to find Tan θ. (so cover Tan θ) 12 cm 𝑇𝑎𝑛 θ= 𝑂 𝐴 𝑇𝑎𝑛 𝑥= 12 9 𝑥 𝑇𝑎𝑛 −1 12 9 𝑥= =53.13° 9 cm (A)

TOA 𝑥 (O) (A) 9 cm 7 cm 𝑇𝑎𝑛 θ= 𝑂𝑝𝑝 𝐴𝑑𝑗 O A 𝑇𝑎𝑛 θ= 𝑂 𝐴 𝑇𝑎𝑛 𝑥= 9 7 Label the sides. Write the formula. Substitute & calculate. 𝑇𝑎𝑛 θ= 𝑂𝑝𝑝 𝐴𝑑𝑗 Find the value of 𝑥 to 2dp. O Tan θ A (O) (A) 9 cm 7 cm We want to find Tan θ. (so cover Tan θ) 𝑥 𝑇𝑎𝑛 θ= 𝑂 𝐴 𝑇𝑎𝑛 𝑥= 9 7 𝑇𝑎𝑛 −1 9 7 𝑥= =52.13°

TOA 𝑥 5 cm 9 cm (O) (A) 𝑇𝑎𝑛 θ= 𝑂𝑝𝑝 𝐴𝑑𝑗 O A 𝑇𝑎𝑛 θ= 𝑂 𝐴 𝑇𝑎𝑛 𝑥= 5 9 Label the sides. Write the formula. Substitute & calculate. 𝑇𝑎𝑛 θ= 𝑂𝑝𝑝 𝐴𝑑𝑗 Find the value of 𝑥 to 2dp. O Tan θ A 𝑥 We want to find Tan θ. (so cover Tan θ) 5 cm 9 cm 𝑇𝑎𝑛 θ= 𝑂 𝐴 𝑇𝑎𝑛 𝑥= 5 9 (O) (A) 𝑇𝑎𝑛 −1 5 9 𝑥= =29.05°

TOA 𝑥 5 cm (O) (A) 8 cm 𝑇𝑎𝑛 θ= 𝑂𝑝𝑝 𝐴𝑑𝑗 O A 𝑇𝑎𝑛 θ= 𝑂 𝐴 𝑇𝑎𝑛 𝑥= 5 8 Label the sides. Write the formula. Substitute & calculate. 𝑇𝑎𝑛 θ= 𝑂𝑝𝑝 𝐴𝑑𝑗 Find the value of 𝑥 to 2dp. O Tan θ A 5 cm (O) (A) We want to find Tan θ. (so cover Tan θ) 8 cm 𝑇𝑎𝑛 θ= 𝑂 𝐴 𝑇𝑎𝑛 𝑥= 5 8 𝑥 𝑇𝑎𝑛 −1 5 8 𝑥= =32.01°

TOA 𝑥 (O) 12 cm 5 cm (A) 𝑇𝑎𝑛 θ= 𝑂𝑝𝑝 𝐴𝑑𝑗 O A 𝑇𝑎𝑛 θ= 𝑂 𝐴 𝑇𝑎𝑛 𝑥= 12 5 Label the sides. Write the formula. Substitute & calculate. 𝑇𝑎𝑛 θ= 𝑂𝑝𝑝 𝐴𝑑𝑗 Find the value of 𝑥 to 2dp. O Tan θ A (O) 12 cm We want to find Tan θ. (so cover Tan θ) 𝑇𝑎𝑛 θ= 𝑂 𝐴 𝑇𝑎𝑛 𝑥= 12 5 𝑥 5 cm (A) 𝑇𝑎𝑛 −1 12 5 𝑥= =67.38°

TOA 𝑥 (O) 4 cm 8 cm (A) 𝑇𝑎𝑛 θ= 𝑂𝑝𝑝 𝐴𝑑𝑗 O A 𝑇𝑎𝑛 θ= 𝑂 𝐴 𝑇𝑎𝑛 𝑥= 4 8 Label the sides. Write the formula. Substitute & calculate. 𝑇𝑎𝑛 θ= 𝑂𝑝𝑝 𝐴𝑑𝑗 Find the value of 𝑥 to 2dp. O Tan θ A (O) 4 cm We want to find Tan θ. (so cover Tan θ) 𝑥 𝑇𝑎𝑛 θ= 𝑂 𝐴 𝑇𝑎𝑛 𝑥= 4 8 8 cm (A) 𝑇𝑎𝑛 −1 4 8 𝑥= =26.57°

TOA 𝑥 (A) 10 cm 11 cm (O) 𝑇𝑎𝑛 θ= 𝑂𝑝𝑝 𝐴𝑑𝑗 O A 𝑇𝑎𝑛 θ= 𝑂 𝐴 𝑇𝑎𝑛 𝑥= 11 10 Label the sides. Write the formula. Substitute & calculate. 𝑇𝑎𝑛 θ= 𝑂𝑝𝑝 𝐴𝑑𝑗 Find the value of 𝑥 to 2dp. O Tan θ A (A) 10 cm 𝑥 We want to find Tan θ. (so cover Tan θ) 𝑇𝑎𝑛 θ= 𝑂 𝐴 𝑇𝑎𝑛 𝑥= 11 10 11 cm (O) 𝑇𝑎𝑛 −1 11 10 𝑥= =47.73°

TOA 𝑥 (A) 13 cm 8 cm (O) 𝑇𝑎𝑛 θ= 𝑂𝑝𝑝 𝐴𝑑𝑗 O A 𝑇𝑎𝑛 θ= 𝑂 𝐴 𝑇𝑎𝑛 𝑥= 8 13 Label the sides. Write the formula. Substitute & calculate. 𝑇𝑎𝑛 θ= 𝑂𝑝𝑝 𝐴𝑑𝑗 Find the value of 𝑥 to 2dp. O Tan θ A 𝑥 (A) We want to find Tan θ. (so cover Tan θ) 13 cm 𝑇𝑎𝑛 θ= 𝑂 𝐴 𝑇𝑎𝑛 𝑥= 8 13 𝑇𝑎𝑛 −1 8 13 𝑥= =31.61° 8 cm (O)

TOA 𝑥 (A) 11 cm 20 cm (O) 𝑇𝑎𝑛 θ= 𝑂𝑝𝑝 𝐴𝑑𝑗 O A 𝑇𝑎𝑛 θ= 𝑂 𝐴 𝑇𝑎𝑛 𝑥= 20 11 Label the sides. Write the formula. Substitute & calculate. 𝑇𝑎𝑛 θ= 𝑂𝑝𝑝 𝐴𝑑𝑗 Find the value of 𝑥 to 2dp. O Tan θ A (A) 11 cm 𝑥 We want to find Tan θ. (so cover Tan θ) 𝑇𝑎𝑛 θ= 𝑂 𝐴 𝑇𝑎𝑛 𝑥= 20 11 20 cm (O) 𝑇𝑎𝑛 −1 20 11 𝑥= =61.19°

TOA 𝑥 14 cm (O) 3 cm (A) 𝑇𝑎𝑛 θ= 𝑂𝑝𝑝 𝐴𝑑𝑗 O A 𝑇𝑎𝑛 θ= 𝑂 𝐴 𝑇𝑎𝑛 𝑥= 14 3 Label the sides. Write the formula. Substitute & calculate. 𝑇𝑎𝑛 θ= 𝑂𝑝𝑝 𝐴𝑑𝑗 Find the value of 𝑥 to 2dp. O Tan θ A We want to find Tan θ. (so cover Tan θ) 14 cm 𝑇𝑎𝑛 θ= 𝑂 𝐴 𝑇𝑎𝑛 𝑥= 14 3 𝑥 (O) 𝑇𝑎𝑛 −1 14 3 3 cm 𝑥= =77.91° (A)

TOA 𝑥 𝑥 𝑥 7 cm 12 cm 5 cm 3 cm 4 cm 5 cm 𝑇𝑎𝑛 θ= 𝑂𝑝𝑝 𝐴𝑑𝑗 O A Label the sides. Write the formula. Substitute & calculate. 𝑇𝑎𝑛 θ= 𝑂𝑝𝑝 𝐴𝑑𝑗 Calculate 𝑥 for these three triangles. (2dp) O Tan θ A 7 cm 𝑥 12 cm 𝑥 5 cm 3 cm 4 cm 𝑥 5 cm

TOA 𝑥 𝑥 𝑥 7 cm 12 cm 5 cm 3 cm 4 cm 5 cm 𝑇𝑎𝑛 θ= 𝑂𝑝𝑝 𝐴𝑑𝑗 O 𝑥=54.46° A Label the sides. Write the formula. Substitute & calculate. 𝑇𝑎𝑛 θ= 𝑂𝑝𝑝 𝐴𝑑𝑗 Calculate 𝑥 for these three triangles. (2dp) O Tan θ A 𝑥=54.46° 7 cm 𝑥 12 cm 𝑥 5 cm 𝑥=30.96° 3 cm 4 cm 𝑥 𝑥=18.43° 5 cm

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