# Trigonometry: math test in 3rd grade (troisième ).

A proctored math assignment on trigonometry in the right triangle. This trigonometry math test is for teachers and students wanting to review their trigonometry chapter online. Trigonometry has a big place in math

Proctored homework: Thales and trigonometry in the right triangle.

## Exercise 1:

In triangle ABC of height [AH] shown below, we give:

AC = 4 cm, AB = 2.5 cm and = 30°.

1. Calculate the exact value of AH.

2. Calculate the measure of the angle rounded to the nearest degree.

3. Deduce the measure of the angle .

## Exercise 2:

We consider the figure opposite which is not in full size.

IJKL is a rectangle.

O, M and I are aligned as well as O, K and J.

The measurements in cm are :

IJ = 7.5; KJ = 3; OK = 1.5

Calculate the exact values of MK and OI, then round OI to the nearest mm.

## Exercise 3 : ‘trigonometry maths

Questions 2, 3 and 4 are independent. The unit is the centimeter.

1. Construct a triangle MAI rectangular in A such that AM = 8 and IM = 12.

2. Calculate the exact value of AI.

3. R is the point of the segment [MI] such that MR = 9.

The parallel to (AI) passing through R intersects [AM] at E.

Calculate ME.

4. Calculate .

Deduct the value, rounded to the nearest degree, of .

## Exercise 4:

From the balcony of my apartment on the second floor of a building, I can see a crane in the construction site opposite.

The building is exactly 19.8 meters from the foot of the crane. Placed at 8 meters above the ground, I determined (with a simple protractor) the angle under which I saw the crane. This angle is equal to 61°.

1. Calling H the point on [BA] such that (OH) and (AB) are perpendicular, and noting that HA = 8 m, calculate the measure of the angle rounded to the nearest degree.

2. Calculate HB to the nearest cm.

3. Deduce the height of the crane to the nearest cm.

## Exercise 5 : ‘trigonometry maths

Let [AB] be a segment, give a method to divide this segment in 5 equal parts using only a non graduated ruler, a non graduated square and a compass.

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