I will Mark you as brainliest if you explain
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This problem requires you to use both kinds of special right triangles.<span>
A 30°-60°-90° t</span>riangle has three angles with measures of 30°, 60°, and 90°. The side lengths are related by a special property, such that the shortest leg (always across from the 30° angle) is y units, the hypotenuse (always across from the 90° angle in every right triangle) is 2y units, and the third leg is
units. (I use y because this is a ratio depending on what we have for y. We can write the simplest ratio as 1:2:√3.)
So it looks like triangle RST is one of these triangles.
If
is the leg across from the 60°-angle, then we have 2√3 = y√3, so y = 2. That means our hypotenuse is 2y = 4.
Now the hypotenuse is one of the legs of the larger right triangle, QRT.
This is a right isosceles triangle, or a 45°-45°-90° triangle. This is given such that the two congruent legs are each y units long, and the hypotenuse is
(or simplified, 1:1:√2).
But we just care about the length of x (side RQ), which we see is the leg that is congruent to RT. The length of RT is 4, so the length of RQ is also 4. Therefore, x = 4.
A 30°-60°-90° t</span>riangle has three angles with measures of 30°, 60°, and 90°. The side lengths are related by a special property, such that the shortest leg (always across from the 30° angle) is y units, the hypotenuse (always across from the 90° angle in every right triangle) is 2y units, and the third leg is
So it looks like triangle RST is one of these triangles.
If
Now the hypotenuse is one of the legs of the larger right triangle, QRT.
This is a right isosceles triangle, or a 45°-45°-90° triangle. This is given such that the two congruent legs are each y units long, and the hypotenuse is
But we just care about the length of x (side RQ), which we see is the leg that is congruent to RT. The length of RT is 4, so the length of RQ is also 4. Therefore, x = 4.