Help me please with "Applying Right Triangles" and Trig

[disneywaltz]

Hi I have a geometry quiz 7th block today. I missed two days because I had the flu, and the only thing I have to help me is my textbook. I am learning Applying Right Triangles and Trig (Chapter 8). If I'm given a problem like this (I need to find the value of X and Y), what would I do?? Thank you

 

[MarkFL]

The largest triangle (presumably a right triangle) is divided into two smaller right triangles where all 3 triangles are similar. This means we may state:

$\displaystyle \displaystyle \frac{y}{24}=\frac{24}{20}$

So, what do you get upon solving for $\displaystyle y$?

 

[disneywaltz]

Would y be 28.8 because of cross multiplication?

 

[MarkFL]

Would y be 28.8 because of cross multiplication?

Yes, that's what I get.

We also know:

$\displaystyle x+20=y$

So, what is $\displaystyle x$?

 

[Ishuda]

Hi I have a geometry quiz 7th block today. I missed two days because I had the flu, and the only thing I have to help me is my textbook. I am learning Applying Right Triangles and Trig (Chapter 8). If I'm given a problem like this (I need to find the value of X and Y), what would I do?? Thank you
View attachment 7739

As stated, there is no solution. Assuming a right triangle, you can find the height h of the [20, h, 24] triangle from the Pythagorean Theorem but x could be as short as '0' or as long as 'infinity' and h would remain the same.

If we do make the assumption of three right triangles [x, h, c], [24, c, y], and [20, h, 24] where the third of the triplets is the hypotenuse, we can start by writing the Pythagorean Theorem for the three triangles
c² = x² + h²
y² = c² + 24²
24² = h² + 20²
Since we are also given
x = y - 20
we have enough information to solve the system without assuming similarity of triangles.

 

[MarkFL]

If we assume a right triangle, then similarity follows from that assumption...it's not a separate assumption.