Question

В прямоугольном треугольнике АВС катет ВС=3, угол А=30 градусам Найдите катет АС

Answer 1

Если один из углов прямоугольного треугольника равен 30 гр,то противолежащий этому углу катет равен половине гипотенузы; Значит АВ= 2* ВС. АВ= 2*3=6 см. По теореме Пифагора АС^2 = АВ^2-ВС^2. АС^2 = 6^2-3^2= 36-9=25. АС= 5 см

Answer 2

Finding the Length of Side AC in a Right Triangle

To find the length of side AC in a right triangle ABC, where BC is the given side length of 3 units and angle A is 30 degrees, we can use trigonometric ratios.

In a right triangle, the sine, cosine, and tangent ratios can be used to relate the angles and side lengths. Since we know the length of side BC and the measure of angle A, we can use the sine ratio to find the length of side AC.

The sine ratio is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this case, side BC is opposite angle A, and side AC is the hypotenuse.

The sine ratio can be expressed as:

sin(A) = BC / AC

To find the length of side AC, we can rearrange the equation:

AC = BC / sin(A)

Substituting the given values, where BC = 3 units and angle A = 30 degrees:

AC = 3 / sin(30°)

Now, let's calculate the value of AC.

Using the trigonometric function sin(30°), we can find that sin(30°) = 0.5.

Substituting this value into the equation:

AC = 3 / 0.5 = 6 units

Therefore, the length of side AC in the right triangle ABC is 6 units.