Cosinus: 4th grade math exercises corrected in PDF.

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1 Series of exercises on the Cosine

Cosine of an acute angle with corrected 4th grade math exercises is very beneficial for the student. Indeed, the latter will have to know his formula for the cosine of an angle in a right triangle. In addition, it allows you to develop geometry and math skills by determining either a length in a right triangle or the measure of one of the acute angles. With this cosine, you will discover a new method of problem solving.
In addition, trigonometry studies triangles and the relationships between the lengths of their sides and the angles at their vertices.
This chapter gives us a new tool to work with the right-angled triangle and the correction allows the student to identify their errors in order to progress in mathematics and develop skills on the cosine in fourth grade on materials similar to your textbook.

Series of exercises on the Cosine

Exercise #1:

1) Construct a rectangle ABC at A knowing that :

AB = 6 cm and $\widehat{ABC}$ = 35°.

2) Calculate the length BC and the length AC; results are given to the nearest millimeter.

Angle	Cosinus
35°	0,819

Exercise #2:

We want to measure the height of a cathedral. Thanks to a measuring instrument placed in O, 1.5 m from the ground and 85 m from the cathedral, we measure the angle $\widehat{COB}$ and we find 59°.

1) Determine the length CB to the nearest tenth of a meter.

2) Deduce the height of the cathedral and round it off to the nearest meter.

Exercise #3:

ABC is a right triangle at A.

We give AB = 5 cm and $\widehat{ABC}$ = 35°.

1) Construct the figure in full size.

2) Determine the length AC, rounded to the tenth of a centimeter.

Exercise 4 Cosine :

A 6 meter ladder is leaning against a 7 meter high vertical wall. For safety reasons, it is estimated that the angle between the ladder and the ground should be 75° (see diagram below).

l) Calculate the distance AB between the foot of the ladder and the wall. (The result will be given rounded to the nearest centimeter).

2) How far CD from the top of the wall is the top of the ladder? (The result will be given rounded to the nearest centimeter).

Exercise #5:

Draw a circle C with center O and radius 4 cm. Draw [AB], a diameter of C.

Place a point E on the circle C such that: $\widehat{BAE}$ = 40°.

1) Show that the triangle ABE is rectangular.

Calculate the exact value of BE and then round it to the nearest millimeter.

2) Locate the point D that is symmetrical to B about E.

Show that the lines (AD) and (OE) are parallel.

3) What is the nature of triangle ABD? Justify.

Exercise #6:

A 20 m long cable is stretched between the top of a vertical pole and the horizontal ground. It forms an angle of 40° with the ground (see diagram).

1. Calculate the height of the pole.

2. Represent the situation by a figure to scale $\frac{1}{200}$ (the data of the situation must be placed on the figure).

Exercise 7 Cosine :

ABCD is a rectangle such that AB = 7.2 cm and BC = 5.4 cm.

1) Draw the rectangle and its diagonal in real size [AC].

2) Calculate the measure, rounded to the nearest degree, of the angle $\widehat{ACD}$ .

3) Show that the angles $\widehat{ACD}$ and $\widehat{CAB}$ are equal.

4) The perpendicular bisector of the segment [AC] intersects the line (AB) at E. Place the point E and show that the triangle ACE is isosceles.

5) Deduce an approximate value for the measure of the angle .

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