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# Trigonometry - PowerPoint PPT Presentation

Trigonometry. Sample Questions & Solutions. Tangent. cosine. sine. adjacen t. 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.

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## PowerPoint Slideshow about 'Trigonometry' - tibor

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Sample Questions & Solutions

Tangent

cosine

sine

Right Angle

Ө

• 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

a

b

(c)

(b)

(a)

A

A

(e)

A

A

(f)

(d)

A

A

Copy each of the triangles below and label each of the sides and the angle.

(c)

(b)

(a)

A

A

(e)

A

A

(f)

(d)

A

A

Copy each of the triangles below and label each of the sides and the angle.

hyp

opp

opp

hyp

opp

hyp

opp

hyp

opp

opp

hyp

hyp

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

• 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

• 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

• 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°

• 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)

hypotenuse

b

10

b

10

c = 10m

a

60°

b

• 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

Opposite

4

3

4

3

4m opposite

• 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 =

15

c

15

c

15

0.6428

c

15m

40°

b

• 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

• 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

• 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

opposite

hypotenuse

• Sin 30°=

• 0.5 =

• 0.5 x 5.42 = rise

• rise = 2.71m Answer (a)

rise

5.42

5.42m

c

40°

30°

b

• 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 =

= 3.23m

Opposite

2.71

5.42m

c

40°

30°

b

• 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°

3.23m

b

• 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

So 4.694 + 3.23 = span

5.42m

c

2.71m

40°

30°

b

3.23m