Emma

December 21, 2020

Chapters

Exercise 1
Exercise 2
Exercise 3
Exercise 4
Exercise 5
Exercise 6
Solution of exercise 1
Solution of exercise 2
Solution of exercise 3
Solution of exercise 4
Solution of exercise 5
Solution of exercise 6

Exercise 1

Determine the height, h, of the drawing below:

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Exercise 2

Calculate the distance from point A to point B.

Exercise 3

Calculate the distance between points A and B.

Exercise 4

Calculate the radius of the circle circumscribed in a triangle, where $A = 45$ °, $B = 72$ °, and $a = 20m$ .

Exercise 5

The radius of a circle measures $25 m$ . Calculate the angle between the tangents to the circle, drawn at the ends of a chord with a length of $36 m$ .

Exercise 6

The diagonals of parallelogram ABCD measure $10 cm$ (AC) and $12 cm$ (BD), and the angle that they form in the center is 48° 15'. Calculate the length of the sides AD and AB.

Solution of exercise 1

Determine the height, h, of the drawing below:

$ABC = 180 - (72\circ 18' + 60\circ 32') = 47\circ 10'$

$\frac { c }{ \sin { (60 \circ 32') }} = \frac { 500 }{ \sin { 47 \circ 10'} } \qquad c = 593.62 m$

$h = 593.62 \times \sin { 62 \circ 5' } = 524.54 m$

Solution of exercise 2

Calculate the distance from point A to point B.

$B = 180 \circ - (61 \circ 28' + 54 \circ 53 ') = 63 \circ 39'$

$\frac { c }{ \sin { 54 \circ 53' } } = \frac { 200 }{ \sin { 63 \circ 39' }}$

$c = 182.565 m$

Solution of exercise 3

Calculate the distance between points A and B.

$\frac { AC }{ \sin { 43 \circ 52' }} = \frac { 450 }{ \sin { 67 \circ 57 ' }} \qquad AC = 336.45 m$

$\frac { CB }{ \sin { 80 \circ 40' }} = \frac { 450 }{ \sin { 66 \circ 44' } } \qquad CB = 483.35m$

${ x }^{ 2 } = { 336.45 }^{ 2 } + { 483.35 }^{ 2 } - 2 \times 336.45 \times 483.35 \times \cos { (68 \circ 11' - 32 \circ 36' ) }$

$x = 286.902 m$

Solution of exercise 4

Calculate the radius of the circle circumscribed in a triangle, where A = $45$ °, B = $72$ °, and a = $20m$ .

$\frac { a }{ \sin A } = 2R$

$R =\frac { 20 }{ 2 \sin { 45 }} = 14.14m$

Solution of exercise 5

The radius of a circle measures $25 m$ . Calculate the angle between the tangents to the circle, drawn at the ends of a chord with a length of $36 m$ .

${ 36 }^{ 2 } = { 25 }^{ 2 } + { 25 }^{ 2 } - 2 \times 25 \times 25 \cos { O } \qquad O = 92 \circ 6' 32''$

In the quadrilateral, AOBT, angles A and B are right angles.

$O + T = 180 \circ$

$T = 180 \circ - 92 \circ 6' 32'' = 87 \circ 53' 28''$

Solution of exercise 6

The diagonals of parallelogram ABCD measure $10 cm$ (AC) and $12 cm$ (BD), and the angle that they form in the center is 48° 15'. Calculate the length of the sides AD and AB.

$AD = \sqrt { { 5 }^{ 2 } + { 6 }^{ 2 } - 2 . 5 . 6 \cos { (48 \circ 15') } } = 4.5877 cm$

$180 \circ - 48 \circ 15' = 131 \circ 45'$

$AB = \sqrt { { 5 }^{ 2 } + { 6 }^{ 2 } - 2 . 5 . 6 \cos { (131 \circ 45' ) } } = 10.047 cm$

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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.

Oblique Triangle Word Problems

Exercise 1

Exercise 2

Exercise 3

Exercise 4

Exercise 5

Exercise 6

Solution of exercise 1

Solution of exercise 2

Solution of exercise 3

Solution of exercise 4

Solution of exercise 5

Solution of exercise 6

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Trigonometric Values

Trigonometric Identities

Trigonometric Ratios

Trigonometric Functions

Trigonometric Formulas

Systems of Simultaneous Trigonometric Equations

Unit Circle

Sine and Cosine Law

Solving Right Triangles

Even-Odd Identities

Oblique Triangles

Pythagorean Identities

Measurement of Angles

Other Trigonometric Identities

Trigonometric Equations

Cofunction Identities

Trigonometric Identities Problems

Trigonometric Angles Worksheet

Right Triangle Word Problems

Trigonometric Equations Worksheet

Oblique Triangle Word Problems

Exercise 1

Exercise 2

Exercise 3

Exercise 4

Exercise 5

Exercise 6

Solution of exercise 1

Solution of exercise 2

Solution of exercise 3

Solution of exercise 4

Solution of exercise 5

Solution of exercise 6

Cancel reply

Theory

Trigonometric Values

Trigonometric Identities

Trigonometric Ratios

Trigonometric Functions

Trigonometric Formulas

Systems of Simultaneous Trigonometric Equations

Unit Circle

Sine and Cosine Law

Solving Right Triangles

Even-Odd Identities

Oblique Triangles

Pythagorean Identities

Measurement of Angles

Other Trigonometric Identities

Trigonometric Equations

Cofunction Identities

Exercises

Trigonometric Identities Problems

Trigonometric Angles Worksheet

Right Triangle Word Problems

Trigonometric Equations Worksheet