Question

У трикутнику ABC кут C = 90° AC = 12 см sin A = 4 / 5 обчислити периметр ABC СРОЧНО ПРОШУ!​

Answer 1

Ответ:     Р Δ = 48 см .

Объяснение:

 cosA =√( 1 - sin²A) = √( 1 - ( 4/5 )² ) = √ ( 1 - 16/25 ) = √( 9/25 ) = 3/5 .

 cosA = AC/AB ;  AB = AC/cosA = 12 : 3/5 = 20 ( см ) .

 sinA = BC/AB ;   BC = ABsinA = 20 * 4/5 = 16 ( см ) .

 Р Δ = a + b + c = 16 + 12 + 20 = 48 ( cм ) ;   Р Δ = 48 см .

Answer 2

Problem Analysis

We are given a triangle ABC with angle C equal to 90 degrees, side AC measuring 12 cm, and sin(A) equal to 4/5. We need to calculate the perimeter of triangle ABC.

Solution

To find the perimeter of triangle ABC, we need to know the lengths of all three sides. We already know that side AC measures 12 cm. Let's denote the lengths of sides AB and BC as a and b, respectively.

Using the Pythagorean theorem, we can find the length of side AB. In a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, we have:

AB^2 = AC^2 + BC^2

Since angle C is 90 degrees, we can substitute the values we know:

AB^2 = 12^2 + BC^2

Now, let's use the given information that sin(A) = 4/5. The sine of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this case, we have:

sin(A) = BC / AC

Substituting the known values:

4/5 = BC / 12

We can solve this equation to find the length of side BC:

BC = (4/5) * 12 = 9.6 cm

Now, we can substitute the values of AC and BC into the equation for AB^2:

AB^2 = 12^2 + 9.6^2

Simplifying:

AB^2 = 144 + 92.16 AB^2 = 236.16

Taking the square root of both sides:

AB = √236.16 AB ≈ 15.36 cm

Now that we know the lengths of all three sides, we can calculate the perimeter of triangle ABC:

Perimeter = AB + BC + AC Perimeter = 15.36 + 9.6 + 12 Perimeter ≈ 37.96 cm

Therefore, the perimeter of triangle ABC is approximately 37.96 cm.

Answer

The perimeter of triangle ABC is approximately 37.96 cm.