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Ch. 2 - Acute Angles and Right Triangles
Lial - Trigonometry 12th Edition
Lial12th EditionTrigonometryISBN: 9780136552161당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Lial 12th EditionCh. 2 - Acute Angles and Right Triangles문제 11
3장, 문제 11

Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Use the Pythagorean theorem to find the unknown side length. Then find exact values of the six trigonometric functions for angle B. Rationalize denominators when applicable. See Example 1.
Right triangle ABC with right angle at C, sides a=5, b=12, c unknown; find c and trig functions for angle B.
a = 5, b = 12

검증된 단계별 안내
1
Identify the sides of the right triangle ABC, where the right angle is at C. This means sides a and b are the legs, and side c is the hypotenuse opposite the right angle.
Use the Pythagorean theorem to find the length of the hypotenuse c: \(c^2 = a^2 + b^2\). Substitute the given values: \(c^2 = 5^2 + 12^2\).
Calculate \(c^2\) by squaring the given sides: \(c^2 = 25 + 144\). Then express \(c\) as \(c = \sqrt{169}\), but do not simplify further here.
To find the six trigonometric functions for angle B, first identify the sides relative to angle B: the side opposite B is a, the side adjacent to B is b, and the hypotenuse is c.
Write the six trigonometric functions in terms of a, b, and c: - \(\sin B = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{a}{c}\) - \(\cos B = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{b}{c}\) - \(\tan B = \frac{\text{opposite}}{\text{adjacent}} = \frac{a}{b}\) - \(\csc B = \frac{1}{\sin B} = \frac{c}{a}\) - \(\sec B = \frac{1}{\cos B} = \frac{c}{b}\) - \(\cot B = \frac{1}{\tan B} = \frac{b}{a}\) Substitute the known values for a, b, and c into these expressions and rationalize denominators if necessary.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Pythagorean Theorem

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (side opposite the right angle) equals the sum of the squares of the other two sides. It is expressed as c² = a² + b². This theorem allows you to find the missing side length when two sides are known.
추천 영상:
5:19
Solving Right Triangles with the Pythagorean Theorem

Trigonometric Functions

The six trigonometric functions—sine, cosine, tangent, cosecant, secant, and cotangent—relate the angles of a right triangle to the ratios of its sides. For an angle, these functions are defined using the lengths of the opposite, adjacent, and hypotenuse sides, providing exact values based on the triangle's dimensions.
추천 영상:
6:04
Introduction to Trigonometric Functions

Rationalizing Denominators

Rationalizing denominators involves rewriting a fraction so that its denominator contains no irrational numbers, such as square roots. This is done by multiplying numerator and denominator by a suitable radical to simplify expressions and present answers in a standard, exact form.
추천 영상:
2:58
Rationalizing Denominators
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