Question

Гипотенуза равна 56, а один из острых углов равен 45градусов .найдите S-?

Answer 1

Решение задания смотри на фотографии

Answer 2

Calculation of the Area (S) of a Right Triangle

To find the area (S) of a right triangle, we need to know the length of the hypotenuse (c) and one of the acute angles (θ).

Given: - Hypotenuse (c) = 56 - One of the acute angles (θ) = 45 degrees

We can use the formula for the area of a right triangle:

S = (1/2) * a * b

where a and b are the lengths of the two legs of the right triangle.

To find the lengths of the legs, we can use trigonometric ratios. In this case, we know the hypotenuse (c) and one of the acute angles (θ). The trigonometric ratio for the sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse:

sin(θ) = opposite / hypotenuse

In our case, the opposite side is one of the legs of the right triangle. Let's call it a.

sin(45) = a / 56

Simplifying the equation, we can solve for a:

a = 56 * sin(45)

Using a calculator, we find that sin(45) is approximately 0.7071. Substituting this value into the equation, we get:

a ≈ 56 * 0.7071

Calculating this, we find that a is approximately 39.6.

Now, to find the length of the other leg (b), 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 two legs:

c^2 = a^2 + b^2

Substituting the known values, we have:

56^2 = 39.6^2 + b^2

Simplifying the equation, we can solve for b:

b^2 = 56^2 - 39.6^2

Using a calculator, we find that b^2 is approximately 1344.64. Taking the square root of both sides, we get:

b ≈ √(1344.64)

Calculating this, we find that b is approximately 36.66.

Now that we have the lengths of both legs, we can calculate the area (S) using the formula:

S = (1/2) * a * b

Substituting the values, we have:

S ≈ (1/2) * 39.6 * 36.66

Calculating this, we find that the area (S) of the right triangle is approximately 723.7 square units.

Therefore, the area (S) of the right triangle with a hypotenuse of 56 and one of the acute angles equal to 45 degrees is approximately 723.7 square units.

Please note that the calculations provided are approximate due to rounding.

Answer:

The area (S) of the right triangle is approximately 723.7 square units.