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Hey

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What is X?Explain.

Apr 3, 2018

#1
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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, $$x=4$$.

Apr 3, 2018

#1
+349
+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, $$x=4$$.