Question

У трикутнику ABC точка M — середина сторони AC, BMA = 90°, BAM=70°, АС =15 см, ВС= 12 см. Знайдіть кут MBC, довжину МС і АВ. помогите пожалуйста ​

Answer 1

Ответ:

∠MBC =15°, ∠BCA = 75°

Объяснение:

ΔАВС, М - середина стороны ⇒ медиана, ∠BMA = 90° ⇒ высота, ⇒ BM и высота ⇒ ΔАВС равнобедренный ⇒ ∠ВАС = ∠ВСM, ∠MBC = 30°/2 = 15 ( т.к. биссектриса).

∠BCA = (180°-∠ABC) ÷ 2 = (180°-30) ÷ 2 = 75

Answer 2

Given Information:

We are given the following information about triangle ABC: - Point M is the midpoint of side AC. - Angle BMA is 90 degrees. - Angle BAM is 70 degrees. - AC has a length of 15 cm. - BC has a length of 12 cm.

Finding the Angle MBC:

To find the angle MBC, we can use the fact that the sum of the angles in a triangle is 180 degrees. Since we know that angle BMA is 90 degrees and angle BAM is 70 degrees, we can find angle MBC by subtracting the sum of these two angles from 180 degrees.

Let's calculate it: - Angle MBC = 180 degrees - (Angle BMA + Angle BAM) - Angle MBC = 180 degrees - (90 degrees + 70 degrees) - Angle MBC = 180 degrees - 160 degrees - Angle MBC = 20 degrees

Therefore, the angle MBC is 20 degrees.

Finding the Length of MS:

To find the length of MS, we can use the fact that M is the midpoint of AC. This means that MS is half the length of AC.

Let's calculate it: - MS = AC / 2 - MS = 15 cm / 2 - MS = 7.5 cm

Therefore, the length of MS is 7.5 cm.

Finding the Length of AB:

To find the length of AB, we can use the Pythagorean theorem. In right triangle BMA, we know the lengths of two sides: BM and BA. We can use these lengths to find the length of AB.

Let's calculate it: - BM is the hypotenuse of right triangle BMA, so we can use the Pythagorean theorem to find its length: - BM^2 = BA^2 + MA^2 - BM^2 = BA^2 + (AC/2)^2 - BM^2 = BA^2 + (15 cm/2)^2 - BM^2 = BA^2 + 112.5 cm^2

- We also know that BC has a length of 12 cm. Since M is the midpoint of AC, we can assume that BM is perpendicular to AC. This means that triangle BMC is a right triangle. We can use the Pythagorean theorem again to find the length of BM: - BM^2 = BC^2 + MC^2 - BM^2 = 12 cm^2 + (AC/2)^2 - BM^2 = 12 cm^2 + (15 cm/2)^2 - BM^2 = 12 cm^2 + 112.5 cm^2

Since both expressions for BM^2 are equal, we can set them equal to each other and solve for BA:

- BA^2 + 112.5 cm^2 = 12 cm^2 + 112.5 cm^2 - BA^2 = 12 cm^2 - BA = √(12 cm^2) - BA = 3.46 cm (rounded to two decimal places)

Therefore, the length of AB is approximately 3.46 cm.

To summarize: - Angle MBC = 20 degrees - Length of MS = 7.5 cm - Length of AB ≈ 3.46 cm