In Exercises 29–36, find the length x to the nearest whole uni...

Question

In Exercises 29–36, find the length x to the nearest whole unit.

Accepted Answer

Welcome back. Everyone. In this problem, we want to determine the value of X rounded to the nearest integer. Our choices are a 600 units. B 592 units, C 952 units and D 692 units. Now, let's think about it. What do we want to know? We want to find the length of the base of our triangle, which is X and we already know it's perpendicular height 600 units. We also know that this triangle is made up of two separate right triangles. So I'll call the triangle at the top triangle one and the triangle at the bottom triangle two. So if I can figure out the base of triangle one, I'll call it X one and the base of triangle two, let's call it X two, then I can add them together to figure out the length of side X. Now, since both of these are right triangles, that means the trigonometric ratios apply. So let me see if I can use that to figure it out. Let me start with triangle one. So I want to find the value of X one. Now, what do we know about triangle one, it's a right triangle, we have the angle being 35 degrees. And if the angle is right here, then the side 600 units will be the adjacent side. While the side X one will be the opposite side. Now what trigonometric ratio relates the opposite side to the adjacent, that's right, the tangent because the tangent of an anger is the ratio of its opposite side to its adjacent side. So that means I can substitute into my formula, a tangent to figure out the opposite side. X one, our angle is 35 degrees. Our opposite side is X one and our adjacent side is 600. So if 10 35 is equal to X one divided by 600 that means X one would be equal to multiplied by the 10 gent of 35 degrees. I won't work it out any further because I want an exact answer at the end. So let me see if we can go figure out the length of side X two. Now for triangle two, OK, I also have 600 as my adjacent side because it's right beside the angle and I have X two as my opposite side. So it's pretty much similar to triangle one. So I can also use the tangent ratio because this means that the tangent of 16 degrees is going to be equal to X two divided by 600. Therefore, just like what happened in triangle one, X two will be equal to 600 multiplied by the tangent of 16 degrees. No, I have values for X two and X one. So it means that we can find the length of side X because therefore that no means that X, that was equal to X one plus X two is now going to be 600 multiplied by 10, 35 degrees plus multiplied by the ton of 16 degrees. When you work that out in your calculator, you'll end up with approximately 592.17 units. But remember that we wanted it to the nearest integer. So that means we can round it off to the nearest integer, which is 592 units. Therefore, our answer for X is equal to B. Thanks for watching. I hope it helped.

In Exercises 29–36, find the length x to the nearest whole unit.

Key Concepts

Right Triangle Side Lengths

Trigonometric Ratios (Sine, Cosine, Tangent)

Rounding and Approximation

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