The length of the longer leg in the considered 30-60-90 Special Right Triangle is given by: Option 3) 17√3yd
What is a 30-60-90 Special Right Triangle?
The right angled triangle in which, the angles are of the measure 30, 60 and 90 degrees is called 30-60-90 Special Right Triangle.
What is law of sines?
For any triangle ABC, with side measures |BC| = a. |AC| = b. |AB| = c,
we have, by law of sines,
[tex]\dfrac{sin\angle A}{a} = \dfrac{sin\angle B}{b} = \dfrac{sin\angle C}{c}[/tex]
Remember that we took
[tex]\dfrac{\sin(angle)}{\text{length of the side opposite to that angle}}[/tex]
The wider the angle is, the larger the side opposite to is.
For this right angled triangle, the side opposite to 60 degrees angle is larger leg (let it be of x yd), and the side opposite to 30 degrees angle is shorter leg (of 17 yd).
As shown in the image below, using the sine law for non right angles, we get:
[tex]\dfrac{\sin\angle A}{a} = \dfrac{\sin\angle B}{b}\\\\\dfrac{\sin(30^\circ)}{17} = \dfrac{\sin(60^\circ)}{x}\\\\x =\dfrac{17 \times \sin(60^\circ)}{\sin(30^\circ)} = 17\sqrt{3} \: \rm yd[/tex]
Thus, the length of the longer leg in the considered 30-60-90 Special Right Triangle is given by: Option 3) 17√3yd
Learn more about law of sines here:
https://brainly.com/question/17289163
