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Carpentry & Joinery Phase 4 Trigonometry Tangent Ө adjacen t cosine sine Right Angle Sample Questions & Solutions

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Carpentry & Joinery Phase 4 Pythagoras Theorem Given a = 3.25m & b = 3.45m calculate the length of c a² + b² = c² 3.25² ² = c² = c² = c² c = √ m Answerc = 4.74m Answer c a b

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Carpentry & Joinery Phase 4Question Copy each of the triangles below and label each of the sides and the angle. A (a) (c) A (b) A (d) A (e) A (f) A

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Carpentry & Joinery Phase 4Answer Copy each of the triangles below and label each of the sides and the angle. A (a) (c) A (b) A (d) A (e) A (f) A hyp adj opp hyp hyp hyp hyp hyp opp opp opp opp adj adj adj adj adj opp

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Carpentry & Joinery Phase 4Question Use your calculator to answer to 4 decimal places (a) cos 25° (b) sin 50° (c) tan 34°

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Carpentry & Joinery Phase 4Answer Use your calculator to answer to 4 decimal places (a) cos 25° (b) sin 50° (c) tan 34° (a) cos 25 = = (b) sin 50 = = (c) tan 34 = =

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Carpentry & Joinery Phase 4Question Use your calculator to find the angles to the nearest degree (a) sin A = 0.83 (b) cos B = ¾ (c) tan A = 5/7

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Carpentry & Joinery Phase 4Answer Use your calculator to find the angles to the nearest degree (a) sin A = 0.83 (b) cos B = ¾ (c) tan A = 5/7 56°(a) 2ndF, sin,.83 = = 56° 41°(b) 2ndF, cos, a/b, 3 ↓ 4 = = 41° 36°(c) 2ndF, tan, a/b, 5 ↓ 7 = = 36°

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Carpentry & Joinery Phase 4 Solving Right-angle Triangles In the triangle below, find the length of b The side we must find is the adjacent (b) We have the hypotenuse c = 10m The ratio that uses adj. & hyp. is cos So cos 60° = = 0.5 = b = 10(0.5) b = 5m Answer c = 10m a b 60° adjacent hypotenuse b 10 b 10

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Carpentry & Joinery Phase 4 Solving Right-angle Triangles Find the angle A to the nearest degree We have the opposite & the adjacent so we use tan ratio Tan A = = Tan A = Use calculator 2ndF, tan, a/b, 4 ↓ 3 = A = A = 53° Answer 3m adjacent 4m opposite A° Opposite adjacent

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Carpentry & Joinery Phase 4 Solving Right-angle Triangles Find the side c (hyp.) to 2 decimal places We are given angle & opposite to find hyp. sin 40° = = x c = 15 c = Answerc = Answer 15m b 40° c 15 c 15 c

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Carpentry & Joinery Phase 4 Solving Right-angle Triangles Given a section through a roof with 2 unequal pitches, calculate (a) the rise of the roof (b) the length of rafter c (c) the span b 30° b 40° c 5.42m

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Carpentry & Joinery Phase 4 Solving Right-angle Triangles This question may seem complicated but we can simplify it by using our knowledge of right-angle triangles Firstly, divide triangle into 2 right-angled triangles (using the rise line) 30° b 40° c 5.42m rise

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Carpentry & Joinery Phase 4 Solving Right-angle Triangles On the larger triangle we have the angle 30° & the hypotenuse 5.42m so we can use ratio sin 30° to find the opposite (rise) Sin = (soh) 30° b 40° c 5.42m oppositehypotenuse

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Carpentry & Joinery Phase 4 Solving Right-angle Triangles Sin 30°= 0.5 = 0.5 x 5.42 = rise 2.71m Answer (a)rise = 2.71m Answer (a) 30° b 40° c 5.42m oppositehypotenuse rise 5.42

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Carpentry & Joinery Phase 4 Solving Right-angle Triangles So on the smaller triangle we now have the opposite (2.71m) and the angle 40° So to find adjacent (part of span) we use Tan Tan 40° = = x adj. = 2.71 adj. = 2.71 ÷ m = 3.23m 30° b 40° c 5.42m 2.71 adjacent adj. Oppositeadjacent

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Carpentry & Joinery Phase 4 Solving Right-angle Triangles Using Pythagoras we can find c a² + b² = c² 2.71² ² = c² = c² c² = c = √ m Answer (b)c = 4.216m Answer (b) 30° b 40° c 5.42m 2.71m 3.23m

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Carpentry & Joinery Phase 4 Solving Right-angle Triangles Using Pythagoras we can find the rest of the span i.e. the base of the larger triangle a² + b² = c² 2.71² + b² = 5.42² b² = b² = – b² = b = √ mb = 4.694m 30°b 40° c 5.42m 2.71m 3.23m

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Carpentry & Joinery Phase 4 Solving Right-angle Triangles So = span 7.924m Answer (c) Span = 7.924m Answer (c) 30°b 40° c 5.42m 2.71m 3.23m

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