Chapters
- Exercise 1
- Exercise 2
- Exercise 3
- Exercise 4
- Exercise 5
- Exercise 6
- Exercise 7
- Exercise 8
- Exercise 9
- Exercise 10
- Exercise 11
- Exercise 12
- Solution of exercise 1
- Solution of exercise 2
- Solution of exercise 3
- Solution of exercise 4
- Solution of exercise 5
- Solution of exercise 6
- Solution of exercise 7
- Solution of exercise 8
- Solution of exercise 9
- Solution of exercise 10
- Solution of exercise 11
- Solution of exercise 12
Exercise 1
The known data for a right triangle ABC is 
and 
. Solve the triangle.
Exercise 2
The known data for a right triangle ABC is 
and 
. Solve the triangle.
Exercise 3
The known data for a right triangle ABC is 
and 
. Solve the triangle.
Exercise 4
The known data for a right triangle ABC is and 
. Solve the triangle.
Exercise 5
A tree 
tall casts a shadow 
long. Find the angle of elevation of the sun at that time.
Exercise 6
An airship is flying at an altitude of 
when it spots a village in the distance with a depression angle of 
. How far is the village from where the plane is flying over?
Exercise 7
Find the radius of a circle knowing that a chord of 
has a corresponding arc of 
.
Exercise 8
Calculate the area of a triangular field, knowing that two of its sides measure 
and 
and between them is an angle of .
Exercise 9
Calculate the height of a tree, knowing that from a point on the ground the top of the tree can be seen at an angle of 
and from 10 m closer the top can be seen at an angle of 
.
Exercise 10
The length of the side of a regular octagon is 
. Find the radii of the inscribed and circumscribed circles.
Exercise 11
Calculate the length of the side and the apothem of a regular octagon inscribed in a circle with a radius of 
centimeters.
Exercise 12
Three towns A, B, and C are connected by roads that form a triangle. The distance from A to C is 
and from B to C, 
. The angle between these roads is 
. How far are towns A and B from each other?
Solution of exercise 1
The known data for a right triangle ABC is and . Solve the triangle.
Solution of exercise 2
The known data for a right triangle ABC is and . Solve the triangle.
Solution of exercise 3
The known data for a right triangle ABC is and . Solve the triangle.
Solution of exercise 4
The known data for a right triangle ABC is and . Solve the triangle.
Solution of exercise 5
A tree tall casts a shadow long. Find the angle of elevation of the sun at that time.
Solution of exercise 6
An airship is flying at an altitude of when it spots a village in the distance with a depression angle of . How far is the village from where the plane is flying over?
Solution of exercise 7
Find the radius of a circle knowing that a chord of has a corresponding arc of .
Solution of exercise 8
Calculate the area of a triangular field, knowing that two of its sides measure and and between them is an angle of .
Solution of exercise 9
Calculate the height of a tree, knowing that from a point on the ground the top of the tree can be seen at an angle of and from 10 m closer the top can be seen at an angle of .
equation 1
equation 2
Putting the value of x in equation 1:
Solution of exercise 10
The length of the side of a regular octagon is . Find the radii of the inscribed and circumscribed circles.
Radius of the inscribed circle.
Radius of the circumscribed circle.
Solution of exercise 11
Calculate the length of the side and the apothem of a regular octagon inscribed in a circle with a radius of centimeters.
Solution of exercise 12
Three towns A, B, and C are connected by roads that form a triangle. The distance from A to C is and from B to C, . The angle between these roads is . How far are towns A and B from each other?
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