Contoh Soal Perbandingan Trigonometri pada segitiga siku siku

Summary

In this video, Sukma Dwi Hartadi explains how to solve trigonometric problems in right-angled triangles using sine, cosine, and tangent functions. Through examples, he demonstrates how to calculate the values of these trigonometric ratios for various angles. He begins by using known side lengths and applies the Pythagorean theorem to find missing sides, before calculating the sine, cosine, and tangent of angles. The video provides clear step-by-step explanations of each calculation, helping viewers understand how to solve similar problems in geometry.

Takeaways

• 😀 The script discusses trigonometric ratios (sine, cosine, and tangent) in right-angled triangles.
• 😀 The first example involves triangle ABC with right angle at C, where the lengths of the sides AB, AC, and BC are provided.
• 😀 To calculate Sin B, Cos B, and Tan B, the formulae used are: Sin B = opposite/hypotenuse, Cos B = adjacent/hypotenuse, and Tan B = opposite/adjacent.
• 😀 In the first example, Sin B is calculated as 3/5, Cos B as 4/5, and Tan B as 3/4.
• 😀 The second example involves another right-angled triangle with known sides BC = 8 cm and AC = 6 cm, and an unknown side AB.
• 😀 The length of side AB is determined using the Pythagorean theorem, resulting in AB = 10 cm.
• 😀 Using the Pythagorean theorem, the relationship between the sides of a right triangle is demonstrated: a² + b² = c².
• 😀 Once AB is known, the trigonometric ratios for angle A can be calculated: Sin A = 6/10, Cos A = 8/10, and Tan A = 6/8.
• 😀 The script highlights the importance of understanding and applying trigonometric ratios in real-world problem-solving scenarios.
• 😀 The overall goal of the lesson is to equip viewers with the ability to solve for sine, cosine, and tangent in right-angled triangles using the given side lengths.

Q & A

What is the main focus of the video?

The video focuses on explaining trigonometric ratios in right-angled triangles, specifically how to calculate sine, cosine, and tangent for given angles.

What are the given values for triangle ABC in the first example?

In triangle ABC, which is right-angled at point C, the given values are AB = 5 cm, AC = 3 cm, and BC = 4 cm.

How is the sine of angle B (Sin B) calculated in the first example?

Sin B is calculated as the ratio of the length of the opposite side (AC) to the hypotenuse (AB), so Sin B = 3/5.

What is the cosine of angle B (Cos B) in the first example?

Cos B is calculated as the ratio of the adjacent side (BC) to the hypotenuse (AB), so Cos B = 4/5.

How is the tangent of angle B (Tan B) determined in the first example?

Tan B is calculated as the ratio of the opposite side (AC) to the adjacent side (BC), so Tan B = 3/4.

In the second example, what is the given information about triangle ABC?

In the second example, the given information includes BC = 8 cm, AC = 6 cm, and the length of side AB is unknown.

How is the length of side AB calculated in the second example?

The length of side AB is calculated using the Pythagorean theorem. The result is AB = 10 cm.

What is the sine of angle A (Sin A) in the second example?

Sin A is calculated as the ratio of the opposite side (AC) to the hypotenuse (AB), so Sin A = 6/10, or 3/5.

What is the cosine of angle A (Cos A) in the second example?

Cos A is calculated as the ratio of the adjacent side (BC) to the hypotenuse (AB), so Cos A = 8/10, or 4/5.

How is the tangent of angle A (Tan A) calculated in the second example?

Tan A is calculated as the ratio of the opposite side (AC) to the adjacent side (BC), so Tan A = 6/8, or 3/4.