Calculer la mesure d'un angle - Trigonométrie 3ème

Summary

This video explains how to calculate an angle in a right-angled triangle using trigonometry. The method 'casse auto' simplifies the process by focusing on the sine, cosine, or tangent of the angle. Through a step-by-step example, the script demonstrates how to apply the sine formula to calculate the angle, ensuring the calculator is set to degree mode. The triangle's sides and the sine formula are used to find the angle, which is then rounded to the nearest degree. The tutorial encourages viewers to practice and share their solutions in the comments.

Takeaways

• 😀 The video teaches how to calculate an angle using trigonometry (sine, cosine, or tangent).
• 😀 The example used is a right triangle with known side lengths (AB = 5 cm, BC = 7 cm).
• 😀 To calculate the angle ACB, you can use the 'casse auto' method to choose the right formula.
• 😀 It's essential to draw a diagram to visualize the triangle and the problem.
• 😀 The 'sin' formula is used here because the opposite side (AB) and the hypotenuse (BC) are known.
• 😀 The mnemonic 'SOH' helps remember the formula for sine: 'sin(angle) = opposite/hypotenuse'.
• 😀 The angle ACB is calculated by finding the sine inverse of the ratio 5/7.
• 😀 Make sure your calculator is in degree mode before calculating the inverse sine.
• 😀 The Casio calculator requires you to ensure it's set to degrees by selecting the appropriate options.
• 😀 After calculating, you find that angle ACB is approximately 46 degrees when rounded.
• 😀 The video encourages viewers to practice and share their answers in the comments.

Q & A

What is the main objective of this video?

The main objective of the video is to explain how to calculate the measure of an angle in a right triangle using trigonometry, specifically using sine, cosine, or tangent formulas.

What is the 'Casse Auto' method?

'Casse Auto' is a method designed to simplify the process of selecting the right trigonometric formula (sine, cosine, or tangent) based on the sides of the triangle and the angle you are trying to find.

Which sides of the triangle are used to calculate the angle?

In a right triangle, the sides used to calculate the angle are the 'opposite' side (the side opposite the angle) and the 'hypotenuse' (the longest side of the triangle, opposite the right angle).

What does the acronym SOH stand for in trigonometry?

SOH stands for 'Sine = Opposite / Hypotenuse,' which is a mnemonic to remember the formula for sine in trigonometry.

What is the first step in solving the problem using trigonometry?

The first step is to carefully read the problem statement to identify the given information, such as the sides of the triangle and the angle to be calculated.

How do you know which formula to use in this case?

By identifying the sides that are given and the one you need to find, you can use the 'Casse Auto' method to determine which formula (sine, cosine, or tangent) is appropriate. In this case, the sine formula is used.

What formula is used to find the angle ACB in the triangle?

The sine formula is used: Sin(ACB) = Opposite / Hypotenuse, which in this case is Sin(ACB) = AB / BC = 5 / 7.

What is the role of the calculator in solving the angle?

The calculator is used to find the inverse sine (arc sine) of the ratio 5/7 to determine the measure of angle ACB. The calculator should be in degree mode for the correct result.

What should you check before using the calculator?

Before using the calculator, make sure it is set to degree mode, as the result should be expressed in degrees. This can be verified or adjusted in the calculator settings.

What is the final result for angle ACB?

The final result for angle ACB, rounded to the nearest degree, is approximately 46°.