Trigonometry
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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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Trigonometry

Trigonometry

Sample Questions & Solutions

Tangent

cosine

sine

adjacent

Right Angle

Ө


Pythagoras theorem

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


Trigonometry

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.


Trigonometry

Answer

(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.

adj

hyp

opp

opp

hyp

opp

hyp

adj

adj

adj

adj

opp

hyp

opp

adj

opp

hyp

hyp


Question

Question

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


Answer

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


Question1

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


Answer1

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

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 triangles1

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

3m adjacent

4m opposite


Solving right angle triangles2

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 triangles3

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 triangles4

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 triangles5

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 triangles6

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 triangles7

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

40°

30°

b

adj.


Solving right angle triangles8

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 triangles9

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 triangles10

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


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