Trigonometry

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# Trigonometry - PowerPoint PPT Presentation

Trigonometry. Sample Questions &amp; Solutions. Tangent. cosine. sine. adjacen t. Right Angle. Ө. Pythagoras Theorem. Given a = 3.25m &amp; 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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Presentation Transcript
Trigonometry

Sample Questions & Solutions

Tangent

cosine

sine

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

a

b

Question

(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

Question
• 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

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

• 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)

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

Opposite

4

3

4

3

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 =

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

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

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 =

= 3.23m

Opposite

2.71

5.42m

c

40°

30°

b

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°

3.23m

b

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

5.42m

c

2.71m

40°

30°

b

3.23m