The ratio of side opposite to the angle A and hypotenuse will be equal to sin30 or [tex]\dfrac{1}{2}[/tex] for all the cases.
Given information:
The given triangle is a right-angled triangle with one angle 30 degrees.
It is required to find the ratio of side opposite to the angle A or 30 degree angle and hypotenuse. This ratio is defined as sin of angle A.
For scale factor of 1, the value of required ratio will be,
[tex]sinA=\dfrac{side}{hypotenuse}\\sin30=\dfrac{1}{2}[/tex]
Now, the scale factor is changed to 3. So, all the sides will increase in the same ratio and hence the required ratio will be the same. This can also be justified as the value of angle A is 30 degrees always.
The value of required ratio will be,
[tex]sinA=\dfrac{side}{hypotenuse}\\sin30=\dfrac{1}{2}[/tex]
For the third case also, the value of sin30 will be same,
[tex]sinA=\dfrac{side}{hypotenuse}\\sin30=\dfrac{1}{2}[/tex]
Therefore, the ratio of side opposite to the angle A and hypotenuse will be equal to sin30 or [tex]\dfrac{1}{2}[/tex] for all the cases.
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https://brainly.com/question/3117474
