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BC=2AD，角ADC为90°，角ACD为75°求角B的度数

To solve this problem, let's break it down step by step.

Given:
- \(\angle ADC = 90^\circ\) (right angle)
- \(\angle ACD = 75^\circ\)
- \(BC = 2 \times AD\)
- We need to find \(\angle ABC\).

### Step 1: Determine \(\angle DAC\)

Since \(\angle ADC\) is a right angle and \(\angle ACD = 75^\circ\), we can find \(\angle DAC\) using the fact that the angles in a triangle sum up to \(180^\circ\).

\[
\angle DAC = 180^\circ - 90^\circ - 75^\circ = 15^\circ
\]

### Step 2: Use the ratio \(BC = 2 \times AD\)

This is an important relationship that will help us. In right triangle \(\triangle ADC\), using trigonometric ratios:

\[
\tan(\angle DAC) = \frac{AD}{DC}
\]

Using this and the given ratio \(BC = 2 \times AD\), we can write:

\[
\tan(\angle BAC) = \frac{AD}{BD} = 2 \times \frac{AD}{DC}
\]

### Step 3: Apply trigonometric identities to find \(\angle B\)

Now, \(\angle ABC\) can be calculated using the fact that the sum of angles in triangle \(\triangle ABC\) must

Explore how to find angle B in triangle ABC given specific angles and the ratio BC = 2 * AD. This problem involves trigonometric ratios and the sum of angles in a triangle theorem. Suitable for students in Grades 9-10.

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