Trigonometry in the triangle with corrected 3rd grade math exercises.

In this series of exercises, you will find the following concepts:

1. right triangle: adjacent side, opposite side and hypotenuse;
2. cosine (cos) of an acute angle;
3. sine (sin) of an acute angle;
4. tangent (tan) of an acute angle;
5. algebraic formula in trigonometry;
6. right triangle, trigonometry and acute angle.

Trigonometry is a branch of mathematics that studies the relationships between the lengths and angles of triangles. It is often used to solve problems in geometry or physics.

These corrected math exercises on trigonometry in the right-angled triangle were written by a math teacher and are available to view online or download in PDF format.

Exercise 1:

To propel balls, Mathieu built an inclined plane of 30° whose

base is 15 cm long.

What is the length of the slope?

Give the rounding to the millimeter.

Exercise 2:

Knowing that the points E, F and G are aligned, we want to calculate the length FS.

1.Calculate the measure of the angle .

2.Calculate the measure of the angle .

3.deduce the rounding to the tenth of FS.

Exercise 3:

a. Use the data in this figure to approximate to the nearest degree the
measure of the angle .

b. Deduce an approximate value for the measure of the angle .

Exercise 4:

Tania flies her kite.
The string has a length TC of 40 m.

It is stretched and the kite is 35 m from the ground.
Give a value approximating to the nearest degree the measure of the angle .

Exercise 5:

1. Why is the triangle PGR below rectangular ?

2. Give in irreducible fraction form the value of:
a. b. c.

Exercise 6:

1. In the triangle ABC rectangle in B, which segment is :

a. the hypotenuse ?

b. the side adjacent to the angle ?
c. the side opposite the angle ?
2. In the triangle BHC right-angled at H, which angle has the opposite side :
a. [BH]? b. [CH]?

Exercise 7:

To access her mezzanine, Lola must install a staircase.
With the data in this figure, give a value approximated to the nearest hundredth of the length AB, in m.

Exercise 8:

The One World Trade Center tower was inaugurated in 2014, in New York City, USA.

A person of 1.65 m, located at 100 m from the tower, measures (O represents his eye).

Calculate the height, in m, of this tower to the nearest unit.

Exercise 9:

A surveyor, positioned in A, wishes to calculate the altitude of the summit S of a hill.

His GPS tells him that he is at an altitude of 625 m.

It performs the following measurements:

a. Give a value approximated to the nearest hundredth of the height HS, in m, of the hill.
b. Deduce the altitude of point S.

Exercise 10:

Here is a sectional drawing of one of the two dormers in this house.

Determine an approximate value to the nearest degree of :
a. the measurement of ,
b. the measurement of .

Cette publication est également disponible en : Français (French) العربية (Arabic)

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