Exercise 1

The known data for a right triangle ABC is a = 5 m and B = 41.7°. Solve the triangle.

Exercise 2

The known data for a right triangle ABC is b = 3 m and B = 54.6°. Solve the triangle.

Exercise 3

The known data for a right triangle ABC is a = 6 m and b = 4 m. Solve the triangle.

Exercise 4

The known data for a right triangle ABC is b = 3 m and c = 5 m. Solve the triangle.

Exercise 5

A tree 50 m tall casts a shadow 60 m long. Find the angle of elevation of the sun at that time.

Exercise 6

An airship is flying at an altitude of 800 m when it spots a village in the distance with a depression angle of 12°. 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 24.6 m has a corresponding arc of 70°.

Exercise 8

Calculate the area of a triangular field, knowing that two of its sides measure 80 m and 130 m and between them is an angle of 70°.

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 30º and from 10 m closer the top can be seen at an angle of 60°.

Exercise 10

The length of the side of a regular octagon is 12 m. 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 49 centimeters.

Exercise 12

Three towns A, B and C are connected by roads which form a triangle. The distance from A to C is 6 km and from B to C, 9 km. The angle between these roads is 120°. How far are the towns A and B from each other?

Solution of exercise 1

The known data for a right triangle ABC is a = 5 m and B = 41.7°. Solve the triangle.

Solution of exercise 2

The known data for a right triangle ABC is b = 3 m and B = 54.6°. Solve the triangle.

Solution of exercise 3

The known data for a right triangle ABC is a = 6 m and b = 4 m. Solve the triangle.

Solution of exercise 4

The known data for a right triangle ABC is b = 3 m and c = 5 m. Solve the triangle.

 

Solution of exercise 5

A tree 50 m tall casts a shadow 60 m long. Find the angle of elevation of the sun at that time.

Solution of exercise 6

An airship is flying at an altitude of 800 m when it spots a village in the distance with a depression angle of 12°. 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 24.6 m has a corresponding arc of 70°.

Solution of exercise 8

Calculate the area of a triangular field, knowing that two of its sides measure 80 m and 130 m and between them is an angle of 70°.

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 30º and from 10 m closer the top can be seen at an angle of 60°.

Solution of exercise 10

The length of the side of a regular octagon is 12 m. 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 49 centimeters.

Solution of exercise 12

Three towns A, B and C are connected by roads which form a triangle. The distance from A to C is 6 km and from B to C, 9 km. The angle between these roads is 120°. How far are the towns A and B from each other?

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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.

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