please help me! it's my third time asking

This theorem describes the relationship between the altitude (h) on the hypotenuse in a right triangle and the two line segments (a and b) it creates on the hypotenuse. (a is the shorter segment and b is the longer segment of the hypotenuse).

For the given triangle:

h = the distance between the parking lot and the beach
a = 18 m
b = 32 m

Substituting these values into the formula:

[tex]\dfrac{18}{h}=\dfrac{h}{32}[/tex]

[tex]\implies 18 \cdot 32=h^2[/tex]

[tex]\implies h^2=576[/tex]

[tex]\implies h=\sqrt{576}[/tex]

[tex]\implies h=24 \textsf{ m}[/tex]

So the distance between the beach and the parking lot is 24 m

Part b

We can now use Pythagoras' Theorem to calculate the distance between the parking lot and the refreshment stand.

Pythagoras' Theorem: a² + b² = c²

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

Given:

a = 24
b = 32
c = distance between refreshment stand and parking lot

Substituting these values into the formula:

⇒ 24² + 32² = c²

⇒ c² = 1600

⇒ c = √1600

⇒ c = 40 m

Therefore, the distance between the parking lot and the refreshment stand is 40 m.

Аноним Аноним · Answer 2 · 2022-03-18T11:03:35+01:00

The beach, the parking lot and the refreshment stand are illustrations of similar triangles.

The distance between the spot and the parking lot is 24 m

The distance between the refreshment stand and the parking lot is 40 m

(a) The distance between the spot and the parking lot

Represent this distance with d.

So, the equivalent ratio is:

[tex]\small \bold{ 32: d = d: 18 }[/tex]

Express as fractions

[tex]\small \bold{\frac{32}{d} =\frac{d}{18}}[/tex]

Cross multiply

[tex]\small \bold{ d × d = 32 \times 18 }[/tex]

[tex]\small \bold{d² = 576 }[/tex]

Take square roots

[tex]\small \bold{d = 24 }[/tex]

Hence, the distance between the spot and the parking lot is 24 m

(b) The distance between the refreshment stand and the parking lot

Represent this distance with d.

Using Pythagoras theorem we have:

[tex]\small \bold{ d² = 32² +24² }[/tex]

[tex]\small \bold{d² = 1600 }[/tex]

Take square roots

[tex]\small \bold{ d = 40}[/tex]

Hence, the distance between the refreshment stand and the parking lot is 40 m