Question

В прямоугольном треугольнике АВС (угол С=90) проведена медиана СК.Угол АКС равен 40.Найдите градусную меру угла А. помогите пожалуйста ребят,задача из мониторинга

Answer 1

                           40 градусов

Answer 2

Solution to Finding the Angle Measure of ∠A in Triangle ABC

To find the measure of angle ∠A in triangle ABC, where ∠C = 90° and median CK is drawn with ∠AKC = 40°, we can use the properties of right-angled triangles and medians.

Step 1: Understanding the Problem We have a right-angled triangle ABC, where ∠C = 90°, and a median CK is drawn with ∠AKC = 40°. We need to find the measure of angle ∠A.

Step 2: Using Properties of Right-Angled Triangles In a right-angled triangle, the median drawn to the hypotenuse is half the length of the hypotenuse. This property can help us find the measure of angle ∠A.

Step 3: Applying the Property of Medians in Right-Angled Triangles Since CK is a median in right-angled triangle ABC, CK = 0.5 * AC.

Step 4: Using Trigonometric Ratios We can use trigonometric ratios to find the measure of angle ∠A. Specifically, we can use the tangent ratio, which is defined as the ratio of the opposite side to the adjacent side in a right-angled triangle.

Step 5: Calculating the Measure of Angle ∠A Using the given information and the properties of right-angled triangles, we can calculate the measure of angle ∠A.

Calculation

Let's calculate the measure of angle ∠A using the given information: - ∠AKC = 40° - CK = 0.5 * AC

We can use the tangent ratio to find the measure of angle ∠A: tan(∠A) = opposite/adjacent

Since CK is the opposite side and AC is the adjacent side, we have: tan(∠A) = CK/AC

Substituting the values: tan(∠A) = (0.5 * AC)/AC tan(∠A) = 0.5

To find the measure of angle ∠A, we can use the inverse tangent (arctan) function: ∠A = arctan(0.5)

Using a calculator, we find: ∠A ≈ 26.57°

Conclusion

The measure of angle ∠A in triangle ABC is approximately 26.57 degrees.