IDNLearn.com provides a seamless experience for finding and sharing answers. Our platform offers comprehensive and accurate responses to help you make informed decisions on any topic.
Sagot :
To solve the problem, we need to analyze the properties of a [tex]\(30^\circ-60^\circ-90^\circ\)[/tex] triangle. The sides of a [tex]\(30^\circ-60^\circ-90^\circ\)[/tex] triangle have a specific ratio which is always [tex]\(1 : \sqrt{3} : 2\)[/tex]. Here, the sides are as follows:
1. The side opposite the [tex]\(30^\circ\)[/tex] angle (the short leg) is the smallest and is denoted as [tex]\(x\)[/tex].
2. The side opposite the [tex]\(60^\circ\)[/tex] angle (the long leg) is [tex]\(x\sqrt{3}\)[/tex].
3. The side opposite the [tex]\(90^\circ\)[/tex] angle (the hypotenuse) is the longest and is [tex]\(2x\)[/tex].
Given that the hypotenuse (which is opposite the [tex]\(90^\circ\)[/tex] angle) measures 9 feet, we can use the ratio to find the short leg.
Since the hypotenuse is [tex]\(2x\)[/tex] and it is given to be 9 feet, we can set up the equation:
[tex]\[ 2x = 9 \][/tex]
To find [tex]\(x\)[/tex]:
[tex]\[ x = \frac{9}{2} \][/tex]
Therefore, the measure of the short leg ([tex]\(x\)[/tex]) is:
[tex]\[ x = 4.5 \][/tex]
So, the short leg of the [tex]\(30^\circ-60^\circ-90^\circ\)[/tex] triangle measures 4.5 feet.
1. The side opposite the [tex]\(30^\circ\)[/tex] angle (the short leg) is the smallest and is denoted as [tex]\(x\)[/tex].
2. The side opposite the [tex]\(60^\circ\)[/tex] angle (the long leg) is [tex]\(x\sqrt{3}\)[/tex].
3. The side opposite the [tex]\(90^\circ\)[/tex] angle (the hypotenuse) is the longest and is [tex]\(2x\)[/tex].
Given that the hypotenuse (which is opposite the [tex]\(90^\circ\)[/tex] angle) measures 9 feet, we can use the ratio to find the short leg.
Since the hypotenuse is [tex]\(2x\)[/tex] and it is given to be 9 feet, we can set up the equation:
[tex]\[ 2x = 9 \][/tex]
To find [tex]\(x\)[/tex]:
[tex]\[ x = \frac{9}{2} \][/tex]
Therefore, the measure of the short leg ([tex]\(x\)[/tex]) is:
[tex]\[ x = 4.5 \][/tex]
So, the short leg of the [tex]\(30^\circ-60^\circ-90^\circ\)[/tex] triangle measures 4.5 feet.
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! Discover the answers you need at IDNLearn.com. Thanks for visiting, and come back soon for more valuable insights.