sine Trigonometry cosine adjacent Ө Tangent Right Angle Sample Questions & Solutions Tangent cosine sine adjacent Right Angle Ө

Pythagoras Theorem Given a = 3.25m & b = 3.45m calculate the length of c a² + b² = c² 3.25² + 3.45² = c² 10.5635 + 11.9025 = c² 22.466 = c² c = √22.466 c = 4.74m Answer c a b

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

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

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

Answer Use your calculator to answer to 4 decimal places (a) cos 25° (b) sin 50° (c) tan 34° (a) cos 25 = 0.906307787 = 0.9063 (b) sin 50 = 0.766044443 = 0.7660 (c) tan 34 = 0.674508516 = 0.6745

Question 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

Answer 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 (a) 2ndF, sin, .83 = 56.098738 = 56° (b) 2ndF, cos, a/b, 3 ↓ 4 = 41.40962211 = 41° (c) 2ndF, tan, a/b, 5 ↓ 7 = 35.53767779 = 36°

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 adjacent hypotenuse b 10 b 10 c = 10m a 60° b

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 = 53.1301 A = 53° Answer Opposite adjacent 4 3 4 3 A° 3m adjacent 4m opposite

Solving Right-angle Triangles Find the side c (hyp.) to 2 decimal places We are given angle & opposite to find hyp. sin 40° = 0.6428 = 0.6428 x c = 15 c = c = 23.34 Answer 15 c 15 c 15 0.6428 c 15m 40° b

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 5.42m c 40° 30° b

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) 5.42m c rise 40° 30° b

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) opposite hypotenuse 5.42m c 40° 30° b

Solving Right-angle Triangles Sin 30°= 0.5 = 0.5 x 5.42 = rise rise = 2.71m Answer (a) opposite hypotenuse rise 5.42 5.42m c 40° 30° b

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° = 0.839 = 0.839 x adj. = 2.71 adj. = 2.71 ÷ 0.839 = 3.23m Opposite adjacent 2.71 adjacent 5.42m c 30° 40° b adj.

Solving Right-angle Triangles Using Pythagoras we can find c a² + b² = c² 2.71² + 3.23² = c² 7.3441 + 10.4329 = c² c² = 17.777 c = √17.777 c = 4.216m Answer (b) 5.42m c 2.71m 40° 30° b 3.23m

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 7.344 + b² = 29.376 b² = 29.376 – 7.344 b² = 22.032 b = √22.032 b = 4.694m 5.42m c 2.71m 40° 30° b 3.23m

Solving Right-angle Triangles So 4.694 + 3.23 = span Span = 7.924m Answer (c) 5.42m c 2.71m 40° 30° b 3.23m