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Worksheet: Right Triangle Trigonometry

Q1:

𝐴 𝐡 𝐢 is an isosceles triangle where 𝐴 𝐡 = 𝐴 𝐢 = 9 c m , 𝐴 𝐷 βŸ‚ 𝐡 𝐢 and π‘š ∠ 𝐢 = 3 4 ∘ . Find the length of 𝐡 𝐢 giving the answer to one decimal place.

Q2:

𝐴 𝐡 𝐢 is a triangle where 𝐴 𝐢 = 3 4 c m , 𝐡 𝐢 = 4 0 c m , and π‘š ∠ 𝐢 = 4 6 ∘ . Point 𝐷 lies on 𝐢 𝐡 where 𝐴 𝐷 βŸ‚ 𝐡 𝐢 . Find the height of the triangle drawn from point 𝐡 to βƒ–     βƒ— 𝐴 𝐢 giving the answer to two decimal places.

Q3:

𝐴 𝐡 𝐢 𝐷 is a rectangle where 𝐴 𝐢 = 4 9 . 6 c m and π‘š ∠ 𝐴 𝐢 𝐡 = 2 6 5 4 β€² ∘ . Find the lengths of 𝐴 𝐡 and 𝐡 𝐢 giving the answer to three decimal places.

  • A 𝐴 𝐡 = 4 4 . 2 3 3 c m , 𝐡 𝐢 = 2 5 . 1 6 4 c m
  • B 𝐴 𝐡 = 4 4 . 2 3 3 c m , 𝐡 𝐢 = 2 2 . 4 4 1 c m
  • C 𝐴 𝐡 = 2 5 . 1 6 4 c m , 𝐡 𝐢 = 4 4 . 2 3 3 c m
  • D 𝐴 𝐡 = 2 2 . 4 4 1 c m , 𝐡 𝐢 = 4 4 . 2 3 3 c m