Answer:
With a 30-60-90 triangle, you can find the length of all three sides, even if you only know one. The length of the shortest side (opposite the 30 angle) is always half the length of the hypotenuse. Use this formula to find the third side [tex]a^{2} + b^{2} = c^{2}[/tex]
The sides are 323, 646, 722.25
Step-by-step explanation:
323*2=646
we now know two sides, use this formula to find the third.
[tex]a^{2} + b^{2} = c^{2}[/tex]
[tex]323^{2} + 646^{2} = c^{2}[/tex]
104329 + 4171316 = c^{2}
521645 = c^{2}
[tex]\sqrt{521645} = c[/tex]
722.25 = c
The lengths of the other sides are 646 feet and 722.25 feet.
Given that,
The length of the side opposite the 30-degree angle of a 30-60-90 is 323 ft.
We have to determine
The lengths of the other sides.
According to the question,
The length of the side opposite the 30-degree angle of a 30-60-90 is 323 ft.
The second side is twice the shortest side is,
[tex]\rm b = 2\times a\\\\b = 2 \times 323\\\\ b= 646[/tex]
The measure of the other sides is determined by using the sum of the square of two sides is equal to the third side.
[tex]\rm a^2+b^2=c^2\\\\(323)^2+(646)^2=c^2\\\\104329 + 4171316 = c^{2}\\\\521645 = c^{2}\\\\c = \sqrt{521645}\\\\c = 722.25[/tex]
Hence, The lengths of the other sides are 646 feet and 722.25 feet.
To know more about Trigonometry click the link given below,
https://brainly.com/question/11977436
