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QQQ – Trigonometry Name __________________ 5 An angle in a right-angled triangle is 75°. What is the ratio of the lengths of the opposite side to the hypotenuse? ______________ 1 Determine x. 6 In a right-angled triangle, the opposite side to an angle 𝜃 has length 4 and the hypotenuse has length 5. What is cos(𝜃)? 3 x 35° ______________ x = _________ (to 2dp) 2 Determine y. 7 Determine x (Hint: find the length of the right-most line first) 3 38° y 35° y = _________ (to 2dp) 65° x 3 Determine θ. 3 θ 4 θ = ______° (to 2dp) 4 A cat is stuck at the top of a tree which is 20m high. You have a ladder which is 30m long, and you place the ladder such that the top is right by the cat. What is the angle of inclination of the ladder to the ground? 7 x = ____________ (to 2dp) 8 A cube sits on a table. What is the angle of inclination of the line between a bottom corner and the opposite top corner, relative to the surface of the table? θ θ=_____________ ______° (to 2dp) Score ________ / 8 Award ___________ QQQ – Trigonometry - ANSWERS 1 Determine x. 5 An angle in a right-angled triangle is 75°. What is the ratio of the lengths of the opposite side to the hypotenuse? 0.97 : 1 (the :1 is optional) 3 x 6 In a right-angled triangle, the opposite side to an angle 𝜃 has length 4 and the hypotenuse has length 5. What is cos(𝜃)? 𝟑 𝟓 35° x = 1.72 2 Determine y. 7 Determine x (Hint: find the length of the right-most line first) 3 38° y y = 3.84 35° x 3 Determine θ. 3 θ 4 θ = 36.87° 4 A cat is stuck at the top of a tree which is 20m high. You have a ladder which is 30m long, and you place the ladder such that the top is right by the cat. What is the angle of inclination of the ladder to the ground? 41.81° 65° 7 x = 14.44 8 A cube sits on a table. What is the angle of inclination of the line between a bottom corner and the opposite top corner, relative to the surface of the table? θ θ=35.26°