Math 35
7.6 "Geometric Applications of Radicals"
Objectives:
* Use the Pythagorean Theorem to solve word problems.
* Solve problems involving 45
45
90
and 30
60
90
triangles.
* Use the distance formula to solve problems.
Use the Pythagorean Theorem to Solve Problems
The Pythagorean Theorem:
If a and b are the lengths of the legs of a right triangle and c
is the length of the hypotenuse, then
:
Example 1: (Using the Pythagorean Theorem)
The length of a = 6 f t and c = 10 f t . Find the length b:
Example 2: (Using the Pythagorean Theorem)
To …ght a …re, the forestry department plans to clear a rectangular ABCD …rebreak around the …re. Crews are equipped
with mobile communications that have a 30 yard range. If the length of segment AB = 10 yd and BC = 24 yd; can crews
at points A and C remain in radio contact?
Solve Problems Involving 45
45
90
Triangles
An isosceles right triangle is a right triangle with two legs of equal length. Isosceles right triangles have angle
measures of 45 ; 45 ; and 90 : If we know the length of one leg of an isosceles right triangle, we can use the Pythagorean
Theorem to …nd the length of the hypotenuse.
Page: 1
Notes by Bibiana Lopez
Intermediate Algebra by Tussy and Gustafson
Example 3: (Solving problems involving 45
7.6
45
90
triangles)
If the hypotenuse of an isosceles right triangle is 25 feet long, …nd the length of the legs.
Solve Problems Involving 30
60
90
Triangles
We know that an equilateral triangle is a triangle with three sides of equal length and three 60 angles. We’ll use
this fact and the Pythagorean Theorem to …nd the length of the sides of a 30
Example 4: (Solving problems involving 30
60
60
90
triangle.
90 triangles)
Find the length of the hypotenuse and the length of the longer leg of a 30
Example 5: (Solving problems involving 30
60
60
90 triangle if the shorter leg is 6 cm:
90 triangles)
A patient was instructed to rise his leg to an angle of 60 and hold the position for 10 seconds. If the patient’s leg is 36
inches long, how high o¤ the ‡oor will his foot be when his leg is held at the proper angle?
Page: 2
Notes by Bibiana Lopez
Intermediate Algebra by Tussy and Gustafson
7.6
Use the Distance Formula to Solve Problems
Distance Formula
The distance d between two points with coordinates (x1 ; y1 ) and (x2 ; y2 ) is given by
:
Example 6: (Using the distance formula)
Find the distance between the points ( 2; 3) and (4; 5) :
Example 7: (Using the distance formula)
The telephone cable in the illustration runs from A to B to C to D: How much cable is required to run from A to D directly?
Page: 3
Notes by Bibiana Lopez