+0  
 
0
43
1
avatar

What is X?Explain.

Guest Apr 3, 2018

Best Answer 

 #1
avatar+333 
+2

So, \(\triangle RST\) has two given interior angles, 60o and 90o. Since the sum of the interior angles of a triangle is 180o, we can deduce that the remaining angle has a measure of 30o. This is a special triangle in which the hypotenuse is double the shorter leg, and the longer leg is \(\sqrt{3}\) times the shorter leg. Since \(\overline{RS}\) is the longer leg and has a measure of  \(2\sqrt3\), the measure of \(\overline{ST}\) is \({2\sqrt3\over\sqrt3}=2\). This means that the measure of hypotenuse \(\overline{RT}\) is equal to \(2*2=4\). Now, \(\triangle QRT\) also has two given angles, 45o and 90o. By the same logic as before, the remaining angle has a measure of 45o. This is also a special triangle, in which the two legs are equal, and the hypotenuse is \(\sqrt2\) times the leg. Since \(\overline{RT}\) and \(\overline{ RQ}\) are both legs of the triangle, their measures must be equal. Therefore, \(x=4\).

 

smiley

Mathhemathh  Apr 3, 2018
Sort: 

1+0 Answers

 #1
avatar+333 
+2
Best Answer

So, \(\triangle RST\) has two given interior angles, 60o and 90o. Since the sum of the interior angles of a triangle is 180o, we can deduce that the remaining angle has a measure of 30o. This is a special triangle in which the hypotenuse is double the shorter leg, and the longer leg is \(\sqrt{3}\) times the shorter leg. Since \(\overline{RS}\) is the longer leg and has a measure of  \(2\sqrt3\), the measure of \(\overline{ST}\) is \({2\sqrt3\over\sqrt3}=2\). This means that the measure of hypotenuse \(\overline{RT}\) is equal to \(2*2=4\). Now, \(\triangle QRT\) also has two given angles, 45o and 90o. By the same logic as before, the remaining angle has a measure of 45o. This is also a special triangle, in which the two legs are equal, and the hypotenuse is \(\sqrt2\) times the leg. Since \(\overline{RT}\) and \(\overline{ RQ}\) are both legs of the triangle, their measures must be equal. Therefore, \(x=4\).

 

smiley

Mathhemathh  Apr 3, 2018

28 Online Users

avatar
avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details