Question

Катети прямокутного трикутника дорівнюють 3см і 4 см . Знайти синус кута, протилежного більшому катету?

Answer 1

Объяснение:

решение смотри на фотографии

Answer 2

Finding the Sinus of the Angle Opposite the Larger Cathetus

To find the sine of the angle opposite the larger cathetus in a right-angled triangle, we can use the formula:

sin(θ) = opposite / hypotenuse

Where: - θ is the angle opposite the larger cathetus - "opposite" is the length of the side opposite the angle - "hypotenuse" is the length of the hypotenuse of the triangle

Given that the lengths of the catheti are 3 cm and 4 cm, we can use the Pythagorean theorem to find the length of the hypotenuse.

Calculating the Hypotenuse

Using the Pythagorean theorem, we can calculate the length of the hypotenuse (c) as follows:

c = √(a^2 + b^2)

Where: - a and b are the lengths of the catheti

In this case: - a = 3 cm - b = 4 cm

Calculating: - c = √(3^2 + 4^2) - c = √(9 + 16) - c = √25 - c = 5 cm

So, the length of the hypotenuse (c) is 5 cm.

Finding the Sine of the Angle

Now that we have the lengths of the catheti and the hypotenuse, we can find the sine of the angle opposite the larger cathetus.

Using the formula: sin(θ) = opposite / hypotenuse

In this case: - The larger cathetus is 4 cm, so it is the "opposite" side. - The hypotenuse is 5 cm.

Calculating: sin(θ) = 4 / 5 sin(θ) = 0.8

So, the sine of the angle opposite the larger cathetus is 0.8.