Question

.

Answer 1

When you have a right triangle with an altitude drawn to the hypotenuse, you get two more right triangles. All right triangles are similar.

Answer 2

Part a.
Call the distance from the beach to the parking lot x.
Then in the upper right triangle,
the ratio of long leg : short leg = 32:x
Then in the smaller lower right triangle,
the ratio long leg : short leg = x : 18
Since all the triangles are similar, the ratios of the lengths of corresponding sides are euqual, so
32:x = x:18, or 32/x = x/18
Cross multiply and solve for x.
x = 24, which you have.

Part b.
You need the length of the long leg of the large right triangle, let's call it y. Remember all 3 right triangles in this case are similar.
In the small lower right triangle, the long leg to the short leg ratio is:
24:18
In the largest trianlge, the ratio of the long leg to the small leg is:
y:?
We don;'t have that, but we can get it with the Pythagoras theorem.
The small lower triangle has leg = 18 and leg = 24. We need the hypotenuse, z.
18^2 + 24^2 = z^2
z^2 = 900, so z = 30
Let's get back to:
In the largest trianlge, the ratio of the long leg to the small leg is:
y:30
So 24:18 = y:30, or 24/18 = y/30
Cross multiply and solve for y

Answer 3

I got 40 for y

Answer 4

Correct