Question

g ratios of similar right triangles
reset
scale factor n:
1
∠a = 30° ∠c = 60°
create similar right triangles by changing the scale factor of the right triangle.
when the scale factor is 1, what is the ratio of the side length of the side opposite ∠a and the length of the hypotenuse? 1/2
change the scale factor to 3. what is the ratio of the side length of the side opposite ∠a to the length of the hypotenuse? 1/2
what is the ratio of the side length opposite any 30 - angle and the length of the hypotenuse?

Explanation:

Step1: Recall trigonometric ratio for 30 - 60 - 90 triangle

In a right - triangle with an angle of 30°, the ratio of the side opposite the 30° angle to the hypotenuse is a fixed value.

Step2: Apply the property of similar triangles

Similar triangles have the same angle measures and the ratios of their corresponding sides are equal. For any right - triangle with a 30° angle, the ratio of the side opposite the 30° angle to the hypotenuse is $\frac{1}{2}$, regardless of the scale factor.

Answer:

$\frac{1}{2}$