Trigonometry: corrected 3rd grade math exercises PDF download.

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.

Trigonometry and balls

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 \widehat{GFS}.

2.Calculate the measure of the angle \widehat{SFE}.

3.deduce the rounding to the tenth of FS.

Trigonometry and angle calculation

Exercise 3:

a. Use the data in this figure to approximate to the nearest degree the
measure of the angle \widehat{LJK}.

b. Deduce an approximate value for the measure of the angle \widehat{LKJ}.

Right-angled triangle and trigonometry

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 \widehat{STC}.

Trigonometry in the right triangle.

Exercise 5:

1. Why is the triangle PGR below rectangular ?

Right-angled triangle and trigonometry

2. Give in irreducible fraction form the value of:
a.cos,(\widehat{GPR}) b. sin,(\widehat{GPR}) c. tan(\widehat{,GPR})

Exercise 6:

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

a. the hypotenuse ?

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

Right-angled triangle and trigonometry

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.

Triangle rectangle

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 \widehat{HOP}\,=\,79,5\,^{\circ} (O represents his eye).

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

Trigonometry in the right triangle.

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:

Trigonometry: sine, cosine and tangent.

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.

Trigonometry in the right triangle.

Determine an approximate value to the nearest degree of :
a. the measurement of \widehat{HAC},
b. the measurement of \widehat{HAB}.

See the answer key for this exercise.

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

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