Question

ABC угол равен C равен 90 sinB=4/15,AB=45 Ac-?

Answer 1

Ответ:

AC = 12 ед.

Объяснение:

• Синус угла – это отношение противолежащего (дальнего) катета к гипотенузе

$sin B = \dfrac{AC}{AB} \\\\AC= AB* sin B=\dfrac{45*4}{15} =12$

Answer 2

To solve this problem, we can use the Pythagorean theorem and the sine function.

Given information: ABC is a right angle triangle, with angle C being 90 degrees. sin B = 4/15 AB = 45

Using the Pythagorean theorem, we know 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. In this case, we have:

AB^2 + BC^2 = AC^2

Since angle C is 90 degrees, BC is the side adjacent to angle B, and AC is the hypotenuse.

Substituting the given values, we have:

45^2 + BC^2 = AC^2

2025 + BC^2 = AC^2

To find BC, we can use the sine function. In a right triangle, the sine of an angle 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 B = BC/AC

Substituting the given value of sin B, we have:

4/15 = BC/AC

Cross-multiplying, we get:

15 * BC = 4 * AC

BC = (4/15) * AC

Now, we can substitute this expression for BC into the equation we derived earlier:

2025 + [(4/15) * AC]^2 = AC^2

Expanding and simplifying, we have:

2025 + (16/225) * AC^2 = AC^2

Multiplying through by 225 to eliminate the denominator, we get:

2025 * 225 + 16 * AC^2 = 225 * AC^2

Now, we can solve for AC:

2025 * 225 = (225 - 16) * AC^2

AC^2 = (2025 * 225) / (225 - 16)

AC^2 = 455625 / 209

AC^2 ≈ 2183.97

Taking the square root of both sides, we get:

AC ≈ 46.74

Therefore, the approximate value of AC is 46.74.