Question

найдите неизвестные стороны и углы прямоугольника по следующим данным гипотенуза А = 30 см угол А = 36 градусов

Answer 1

Треугольник АВС- прямоугольный, значит угол С=90градусовугол В=180 градусов-90 градусов-36 градусовугол В=54 градуса

Answer 2

Finding the Unknown Sides and Angles of a Rectangle

To find the unknown sides and angles of a rectangle, we need to use the given information of the hypotenuse (A) and angle (A).

Let's break down the problem step by step:

1. Identify the given information: - Hypotenuse (A) = 30 cm - Angle (A) = 36 degrees

2. Determine the relationship between the given information and the sides and angles of a rectangle: - In a rectangle, the opposite sides are equal in length, and the adjacent angles are equal in measure (90 degrees). - Since we are given the hypotenuse (A) and angle (A), we can use trigonometric ratios to find the other sides and angles.

3. Use trigonometric ratios to find the unknown sides and angles: - We can use the sine, cosine, or tangent ratios to find the unknown sides and angles. Let's use the sine ratio.

- Step 1: Find the length of the adjacent side (B) using the sine ratio: - sin(A) = opposite/hypotenuse - sin(36) = B/30 - B = 30 * sin(36) - B ≈ 17.96 cm

- Step 2: Find the length of the opposite side (C) using the Pythagorean theorem: - In a rectangle, the opposite sides are equal in length. - C = B ≈ 17.96 cm

- Step 3: Find the measure of the other angle (B) using the inverse sine function: - sin(B) = opposite/hypotenuse - sin(B) = C/30 - B = arcsin(C/30) - B ≈ arcsin(17.96/30) - B ≈ 53.13 degrees

4. Summary of the unknown sides and angles of the rectangle: - Length of the adjacent side (B) ≈ 17.96 cm - Length of the opposite side (C) ≈ 17.96 cm - Measure of the other angle (B) ≈ 53.13 degrees

Please note that the above calculations are approximate values based on the given information and trigonometric calculations.