Question

ПОМОГИТЕ ПЛИИИЗ!Найдите длину катета ВС прямоугольного треугольника АВС с прямым углом С,если известно,что:1)АВ =10 см, угол А=60 градусов2)АВ =12 см, угол В=45 градусов3)АС=см, угол А=45 градусов 4)АС=см, угол В=30 градусовмне это нужно до четверга,помогите срочно

Answer 1

1) BC=AB×sin^A=10×sqrt(3)/2=5×sqrt(3)       2) BC=AB×cos^B=12×sqrt(2)/2=6×sqrt(2)      3) BC=AB×tg^A=5×sqrt(2)×1=5×sqrt(2)      4) BC=AC×cos^B=2×sqrt(3)×sqrt(3)/2=3     Условные обозначения:sqrt-квадратный корень, ^-угол, ×-умножить

Answer 2

Finding the Length of the Hypotenuse (AC) of a Right Triangle ABC

To find the length of the hypotenuse (AC) of a right triangle ABC, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Let's consider each given scenario one by one:

Scenario 1: AB = 10 cm, angle A = 60 degrees

In this scenario, we have the length of one side (AB) and the measure of one angle (angle A). To find the length of the hypotenuse (AC), we can use the sine function.

The sine of angle A is defined as the ratio of the length of the side opposite angle A (BC) to the length of the hypotenuse (AC). Therefore, we can write:

sin(A) = BC / AC

Rearranging the equation, we get:

AC = BC / sin(A)

To find BC, we can use the cosine function:

cos(A) = BC / AB

Rearranging the equation, we get:

BC = AB * cos(A)

Substituting the values we have:

AB = 10 cm A = 60 degrees

We can calculate BC using the cosine function:

BC = 10 cm * cos(60 degrees)

Now, we can substitute the values of BC and A into the equation for AC:

AC = BC / sin(A)

Calculating the value of AC using the given values:

AC = (10 cm * cos(60 degrees)) / sin(60 degrees)

Scenario 2: AB = 12 cm, angle B = 45 degrees

In this scenario, we have the length of one side (AB) and the measure of one angle (angle B). We can use similar trigonometric functions to find the length of the hypotenuse (AC).

Using the sine function, we can write:

sin(B) = AC / AB

Rearranging the equation, we get:

AC = AB * sin(B)

Substituting the values we have:

AB = 12 cm B = 45 degrees

We can calculate AC using the sine function:

AC = 12 cm * sin(45 degrees)

Scenario 3: AC = cm, angle A = 45 degrees

In this scenario, we have the length of the hypotenuse (AC) and the measure of one angle (angle A). We can use the cosine function to find the length of the other side (BC).

Using the cosine function, we can write:

cos(A) = BC / AC

Rearranging the equation, we get:

BC = AC * cos(A)

Substituting the values we have:

AC = cm A = 45 degrees

We can calculate BC using the cosine function:

BC = AC * cos(45 degrees)

Scenario 4: AC = cm, angle B = 30 degrees

In this scenario, we have the length of the hypotenuse (AC) and the measure of one angle (angle B). We can use the sine function to find the length of the other side (BC).

Using the sine function, we can write:

sin(B) = BC / AC

Rearranging the equation, we get:

BC = AC * sin(B)

Substituting the values we have:

AC = cm B = 30 degrees

We can calculate BC using the sine function:

BC = AC * sin(30 degrees)

Please provide the value of AC in scenario 3 and scenario 4 so that we can calculate the lengths of the other sides (BC) using the formulas mentioned above.