Learn Advanced Concepts of Indirect Measurement Let’s learn about indirect measurements. The problem says that the triangles in the diagram below are similar and we need to find the value of x, x is here. So let’s look at the similar triangles. The triangles are RSU, we’re starting with right angle coming towards the smaller angle and going up on top. So here also we’ve got to start at the right angle which is here similar to triangle T, come to the smaller angle which is S and go up towards Q. It’s key to make sure that even though the figures maybe arranged however they are, here the corner or the right angle triangle is to the left here it’s to the right. We need to make sure that we know what is the corresponding or which the corresponding sides are. So here RS corresponds to TS, US corresponds to QS sides which means QT on the side is the same as UR this side. These are the corresponding sides. If these triangles are similar, what are we told? That these three sides are equivalent to the ratios of the corresponding sides are equal. What does that mean? Which means RS/TS=US/QS=UR/QT. We are given a bunch of these values. Let’s see what we’re given. What we’re given is RS that’s given to us as 18 meters, TS is given to us as 42 meters equals US is not given to us. QS is not given to us. So this is now out. UR is given to us as 16 meters and QT is given to us as x. This is what we need determine. So I can ignore this part and simply get to 18/42 meters for both sides=16 meters/x. If these are equivalent fractions, I can cross multiply it and the products will be equal. So 18 meters multiplied by x equals 42 meters multiplied by 16 meters. If 18 meters × x = 42 meters×16 meters, I can divide both sides by 18 to get x=42 meters × 16 meters/18 meters. All I did was divide the left side of the equation and the right side of the equation both by 18 meters which gives me 16×42/18=37.3 meters or the missing side x equals 37.3 meters. The key thing that we need to remember is we use the equivalency of the corresponding sides to form this particular expression. Because if the triangles are similar the corresponding sides are equal in ratio, if that’s the case, I can solve for x which is 37.3. Now one thing to remember when we wrote down which sides are corresponding, we looked at this particular angle and this particular angle. And we looked at which sides are indeed the corresponding sides. That’s the key thing. Otherwise, we’ll end up making mistakes.