In each figure, there are two similar triangles. Find the unknown...

Question

In each figure, there are two similar triangles. Find the unknown measurement. Give approximations to the nearest tenth.

Accepted Answer

Welcome back everyone in this problem, we want to solve our age in the following figure of two similar triangles to two decimal places. If necessary for our answer choices. A is 225 centimeters. B is 277.78 centimeters. C is 200 centimeters and the D is 233.33 centimeters. Now, before we continue, let's make sense of our diagram. So we're trying to solve for H which is the hypotenuse of the largest triangle. Both of them are right triangles. And in the larger triangle, it has a base of 25 plus centimeters which is 250 centimeters. In our smaller triangle. It has a base of 225 centimeters. OK. And it has a, the length of its hypotenuse is 250 centimeters. Now, what else do we know? We also know that these are two similar triangles and if two triangles or two figures in general are similar, that means they have the same shape but different sizes that tells us that all sides for the ratio of the larger triangle to the smaller triangle are in the same ratio. So if we can find a ratio of one pair of sides, we can use it to solve for the unknown side in the other. So let's think about it. Do we know any two similar pair of sides? Well, yes, we know the base for both triangles. So since the best or rather let me say since we know the best is or both triangles, that means whatever ratio, the base, the whatever ratio the bases are in is the same ratio that the hypo will be in. So the base of the smaller triangle is 225 and the base of the larger triangle is 250. So that means that would be the same ratio as the base of the smaller hypotenuse, which is 250 to the larger hypotenuse, which is H therefore, we can rewrite our ratio as 225 to 2 equals 250 to H. No, we can go ahead and solve for our unknown value for the hypotenuse. H. So let's do some transposition here. If we multiply both sides by H, then our left hand side will become 225 H divided by 250 equals H counts as H on the right hand side. So that leaves us with 250. Let's do some simplifying here. Both of these, both the numerator and denominator and the left hand side have a common factor of 25. So if we factor 25 out 25 into 225 is nine while into 250 it goes 10 times. Now we can do some more transposition. So we can multiply both sides by 19th by the reciprocal of what we have here. So if we think about it 19th multiply it by what we have, 10 goes into 10, 01 time and nine goes into 91 time. We'll also have to do the same to the left, to the right hand side. So H equals 250 multiplied by 10, which is 2500 divided by nine and divided by nine. When you put that into your calculator, you will get that. It approximately equals 277.7777 and it continues on and on. But remember we said we want our answer to two decimal places if necessary. So it's necessary we need to round it. So when we look at our second decimal place, the number beside it is greater than five. So to two decimal places, the value of each is 277. centimeters. When we look back in our list of choices that would have been answer. Choice. B Thanks a lot for watching everyone. I hope this video helped.

In each figure, there are two similar triangles. Find the unknown measurement. Give approximations to the nearest tenth.

Key Concepts

Similar Triangles

Proportionality

Trigonometric Ratios

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