Question

Найдите неизвестные стороны и острые углы прямоугольного треугольника с катетами 5см и 12 см

Answer 1

По т. Пифагора с²=а²+в² = 12²+5²=144+25=169; с=√169=13 - гипотенуза.
cos∠A=5/13= 0.3846, ∠A≈67°
∠B=90°- 67°= 23°
Ответ: гипотенуза - 13 см, ∠А=67°, ∠В= 23°

Answer 2

Finding the Unknown Sides and Angles of a Right-Angled Triangle

To find the unknown sides and acute angles of a right-angled triangle with the given catheti of 5 cm and 12 cm, we can use the Pythagorean theorem and trigonometric functions.

1. Finding the Hypotenuse (c): Using the Pythagorean theorem, we can find the length of the hypotenuse (c) of the right-angled triangle: a^2 + b^2 = c^2 where a and b are the lengths of the catheti.

Substituting the given values: 5^2 + 12^2 = c^2 25 + 144 = c^2 169 = c^2 c = √169 c = 13 cm 2. Finding the Acute Angles: We can use trigonometric functions to find the acute angles of the right-angled triangle.

a) Angle Opposite to the Cathetus of 5 cm: Using the sine function: sin(A) = opposite/hypotenuse sin(A) = 5/13 A = sin^(-1)(5/13) A ≈ 22.6 degrees b) Angle Opposite to the Cathetus of 12 cm: Using the sine function: sin(B) = opposite/hypotenuse sin(B) = 12/13 B = sin^(-1)(12/13) B ≈ 67.4 degrees Therefore, the unknown sides and acute angles of the right-angled triangle with catheti of 5 cm and 12 cm are: - Hypotenuse (c): 13 cm - Acute Angle Opposite to 5 cm: ≈ 22.6 degrees - Acute Angle Opposite to 12 cm: ≈ 67.4 degrees