Question

Один з гострих кутів прямокутного трикутника дорівнює 21°. Знайдіть кут між бісектрисою і висотою, які проведені з вершини прямого кута.

Answer 1

Відповідь:

24°

Пояснення:

Answer 2

Finding the Angle Between the Bisector and the Altitude in a Right-Angled Triangle

To find the angle between the bisector and the altitude in a right-angled triangle, we can use trigonometric principles.

Given: One acute angle of the right-angled triangle = 21°

We know that in a right-angled triangle, the sum of the two acute angles is 90°. Therefore, the other acute angle can be found using the following equation:

Other acute angle = 90° - 21°

Let's calculate this:

Other acute angle = 90° - 21° = 69°

Now, we have the two acute angles of the right-angled triangle: 21° and 69°.

Next, we need to find the angle between the bisector and the altitude. To do this, we can use the properties of right-angled triangles and trigonometric functions.

The angle between the bisector and the altitude in a right-angled triangle can be found using the following trigonometric relationship:

tan(angle between bisector and altitude) = (tan(A/2)) / (tan(90° - A))

Where: - A = one of the acute angles of the right-angled triangle

Let's substitute the value of A (21°) into the equation and calculate the angle between the bisector and the altitude:

tan(angle between bisector and altitude) = (tan(21°/2)) / (tan(90° - 21°))

Using a calculator or trigonometric tables, we can find the value of the angle between the bisector and the altitude.

This approach will help us determine the angle between the bisector and the altitude in the given right-angled triangle.