Question

в остроугольном треугольнике АВC АВ=2корень2,ВС=3см.площадь трееугольника АВС равна 3см в квадрате .наидите длину стороны АС?Пожалуйста,очень срочно надо,люди помогите!!!!Пожалуйста,очень срочно надо,люди помогите!

Answer 1

S = AB*BC*sin(B)/2; 3 = 2*корень(2)*3*sin(B)/2; sin(B) = 1/корень(2); угол В = 45 градусов; cos(B) = 1/корень(2);

По теореме косинусов

AC^2 = AB^2 + BC^2 - 2*AB*BC*cos(B);

AC^2 = 8 + 9 - 2*2*корень(2)*3*(1/корень(2)) = 8 + 9 - 12 = 5;

AC = корень(5);

Answer 2

Calculation of Side AC in an Acute Triangle

To find the length of side AC in the acute triangle ABC, we can use the Pythagorean theorem. The Pythagorean theorem states that 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 an acute triangle, so we need to find the length of side AC using the given information. We know that AB = 2√2 and BC = 3 cm. Let's denote the length of side AC as x.

According to the Pythagorean theorem, we have:

AB^2 + BC^2 = AC^2

Substituting the given values, we get:

(2√2)^2 + (3)^2 = AC^2

Simplifying the equation, we have:

8 + 9 = AC^2

17 = AC^2

To find the length of side AC, we need to take the square root of both sides of the equation:

√17 = AC

Therefore, the length of side AC in the acute triangle ABC is √17.

Please note that the square root of 17 is an irrational number and cannot be expressed as a simple fraction or decimal.