Question

special right triangles: tutorial
activity
in this activity, you will investigate the basis for the extended ratio of the 30°-60°-90° triangle. to investigate the ratio, we will use an equilateral triangle with a side length of 2. proceed to part a to begin.
part a
on triangle abc, draw the altitude from vertex a to side bc. (recall that an altitude is perpendicular to the line to which it is drawn.) use the text box tool to label the point where the altitude meets side bc as point d. then, determine the measures of ∠bad and ∠adb, and the length of bd. using the text box tool, label the drawing with these measures.

Explanation:

Step1: Identify altitude properties

The altitude from A to BC (point D) is perpendicular to BC, so $\angle ADB = 90^\circ$.

Step2: Find $\angle BAD$

In $\triangle ABC$, $\angle BAC = 60^\circ$. The altitude bisects $\angle BAC$ in an equilateral triangle, so $\angle BAD = \frac{60^\circ}{2} = 30^\circ$.

Step3: Calculate length of $\overline{BD}$

The altitude bisects side BC in an equilateral triangle. Since $BC=2$, $\overline{BD} = \frac{2}{2} = 1$.

Answer:

• $\angle BAD = 30^\circ$
• $\angle ADB = 90^\circ$
• Length of $\overline{BD} = 1$