Math Problem Statement

CONTROLE 8 COSINUS.pdf

140.32 KB

Solution

It looks like you've uploaded a document with some mathematical exercises involving trigonometry, focusing on calculating angles and lengths in right triangles.

Here’s a quick overview of the tasks:

Exercice 1:

  • Triangle ABC is a right triangle at A with sides AB = 4 cm and BC = 7 cm. a. You need to calculate the measure of the angle ∠ABC (denoted as ABC^\hat{ABC}) rounded to the nearest degree. b. Based on that, you'll then deduce the measure of the angle ∠ACB.

Exercice 2:

  • Triangle RST is a right triangle at R, with RT = 4.3 cm and RTS^=55\hat{RTS} = 55^\circ. a. You are asked to calculate the length of side ST, rounded to one decimal place.

Exercice 3:

  • This exercise involves multiple steps.
    1. Calculate the distance BC.
    2. Calculate the approximate angle ∠BA (rounded to the nearest degree).
    3. Calculate the length of side DC, rounded to one decimal place.

Exercice 4:

  • A few more calculations for a right triangle.
    1. Calculate the measure of ∠ACB.
    2. Calculate the length of side AC, rounded to the nearest tenth.
    3. Calculate the length of side BC, rounded to the nearest tenth.

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Right Triangles
Angle Calculation
Side Length Calculation

Formulas

Pythagorean Theorem
Trigonometric Ratios (Sine, Cosine, Tangent)

Theorems

Pythagorean Theorem
Trigonometric Ratios

Suitable Grade Level

Grades 9-11