February 1, 2021

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?