7.3 Use Similar Right Triangles
Hubarth
Algebra
Ex 1 Identify Similar Triangles
Identify the similar triangles in the diagram.
TSU ~
RTU ~
RST
Ex 2 Find the Length of the Altitude to the Hypotenuse
The diagram below shows a cross-section of a swimming pool. What is the
maximum depth of the pool?
Identify the similar triangles and sketch them.
RST ~
RTM ~
TSM
Ex 2 continue
Find the value of h. Use the fact that
TM
ST
h
64
=
=
RST ~
RTM to write a proportion.
TR
SR
152
165
165h = 64(152)
h
59
Read the diagram. You can see that the maximum depth of the pool is h + 48,
which is about 59 + 48 = 107 inches.
The maximum depth of the pool is about 107 inches.
Ex 3 Use a Geometric mean
Find the value of y. Write your answer in
simplest radical form.
length of hyp. of
RPQ
length of hyp. of
RQS
9
y
y
=
27 = y2
27 = 𝑦
3 3=𝑦
3
=
length of shorter leg of
RPQ
length of shorter leg of
RQS
Ex 4 Find the Height Using Indirect Measurement
To find the cost of installing a rock wall in
your school gymnasium, you need to find the
height of the gym wall.
You use a cardboard square to line up the top
and bottom of the gym wall. Your friend
measures the vertical distance from the
ground to your eye and the distance from you
to the gym wall. Approximate the height of
the gym wall.
By Theorem 7.6, you know that 8.5 is the geometric mean of w and 5.
w
8.5
w
8.5
=
5
14.5
So, the height of the wall is 5 + w
5 + 14.5 = 19.5 feet.