Question

В прямоугольном треугольникеABC с прямым углом C проведена высота CD. Найдите выличену угла В,если DA=4,а АС=8 Ответ дайте в градусах Пожалуста...помогите

Answer 1

Ответ:

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Answer 2

Finding the measure of angle B in a right triangle

To find the measure of angle B in a right triangle ABC, where angle C is the right angle and CD is the altitude, we can use trigonometric ratios. In this case, we are given that DA = 4 and AC = 8.

Let's start by labeling the triangle:

      A
     /|
    / |
   /  |
  /   |
 /    |
C_____|B
   D

We know that CD is the altitude, which means it is perpendicular to AB. Therefore, triangle ACD is a right triangle.

Using the Pythagorean theorem, we can find the length of AD:

AD^2 + CD^2 = AC^2

Substituting the given values:

4^2 + CD^2 = 8^2

16 + CD^2 = 64

CD^2 = 64 - 16

CD^2 = 48

Taking the square root of both sides:

CD = √48

Simplifying:

CD = 4√3

Now, let's consider triangle ABD. We can use the trigonometric ratio tangent to find the measure of angle B:

tan(B) = opposite/adjacent

In this case, the opposite side is CD and the adjacent side is AD.

tan(B) = CD/AD

Substituting the given values:

tan(B) = (4√3)/4

Simplifying:

tan(B) = √3

To find the measure of angle B, we can use the inverse tangent function (also known as arctan or tan^(-1)):

B = arctan(√3)

Using a calculator, we find that B is approximately 60 degrees.

Therefore, the measure of angle B in the right triangle ABC is approximately 60 degrees.