Problem

8. △DEF has ∠D=33∘,∠F=75∘, and e=7.5 m. Sketch the triangle. [2 marks]

Answer

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Answer

In triangle DEF, angle D = 33°, angle E = 72°, angle F = 75°, side d ≈ 4.30 m, side e = 7.5 m, and side f ≈ 7.62 m

Steps

Step 1 ：Find the third angle: ∠E=180−∠D−∠F=180−33−75=72∘

Step 2 ：Use the sine rule to find side d: dsin⁡33∘=7.5sin⁡75∘⇒d≈4.30 m

Step 3 ：Use the sine rule to find side f: fsin⁡72∘=7.5sin⁡75∘⇒f≈7.62 m

Step 4 ：In triangle DEF, angle D = 33°, angle E = 72°, angle F = 75°, side d ≈ 4.30 m, side e = 7.5 m, and side f ≈ 7.62 m

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