Chapter 11 Basic Geometry
Math Vic
Math1060HomeworkChapter112Solutions.docxChapter 11 Basic Geometry Homework Name___________________________________
You may use a calculator.
Sketch and label.
1)
Solution:
Acute angles in an angle less than 900
A
B
CA
Find the square root.
2)
324
Solution:
For #3 and #4, find the measure of the requested angle.
3) Find the complement of 41°.
Solution:
Let A be the complement of 41°. Sum of complement angles is 90°. So A+41°=90°
A+90°-41°=49°
Answer: The complement of 41° is 49°
4) What is the measure of the angle that is supplementary to 119°?
Solution:
Let B be the supplementary 119°. Sum of supplementary angles is 180°. So B+119°=61°
A+90°-41°=49°
Answer: The supplementary of 119° is 61°
In a right triangle, find the length of the side not given. Let c represent the length of the hypotenuse. Use correct units in your answer.
5) a = 7 in., b = 24 in.
Solution:
Answer: The length of the hypotenuse is 25 in.
For #6 - #9, find the perimeter and area. Use correct units in your answers.
6) A square with side 1.5 in.
Solution:
Answer: The Perimeter of the Square is 6 in and the area is 2.25 in2.
7) An equilateral triangle with side 25 ft
Solution:
8)
10 m
24 m
Solution:
Answer: The Perimeter of the rectangle is 68 m and the area is 240 m2.
9) The sides are each 3.6 feet in length.
4 ft
3 ft
8 ft
Solution:
Answer: The Perimeter of the trapezoid is 22 ft and the area is 18 ft2.
10) Find the area and circumference. Use correct units in your answers. Use Use u = 3.14 to approximate pi.
14 mi
Solution:
Answer: The Area of the circle is 153.86 mi2 and the circumference of the circle is 43.96 mi2.
11) Find the perimeter. Use correct units in your answer.
7
9 in.
4 in.
5 in.
7 in.
8 in.
Solution:
The perimeter is the sum of all sides:
Answer: The perimeter is 33 in.
For #12 - #13, find the volume. Use u = 3.14 when needed. Use correct units in your answers.
12)
7.5 cm
6.8 cm
4.5 cm
Solution:
The Volume of the Cuboid:
Answer: The volume of the cuboid is 229.5 cm3.
13)
r = 36
ft
Solution:
The Volume of the Sphere:
Answer: The volume of the Sphere is 195333.12 ft3.
For #14 and #15, find the unknown values for side lengths or angle measurements. Use correct units in your answers.
14)
35°
94°
Solution:
The Sum of a triangle add upto 180°:
X+94°+35°=180°
X=180°-94°-35°=51°
Answer: The angle of X is the triangle 51°.
15)
6 cm c
8 cm
Solution:
Answer: The length of side c of the triangle is 10 cm.
The two triangles below are similar. Find x and y.
16)
5.4
3.6
Solution:
Using ratios,
Answer: The length x is 4.2 and y is 3.6.
17) The picture shows the intersection of several streets in a city. Is the angle formed by E Post Street and Sampson Street below Post Street acute or obtuse?
Solution:
Acute angles in an angle less than 900 and obtuse angle is an angle greater than 900 but less than 1800. So the angle formed by E Post Street and Canyon Road S is 900, and since the angle formed by E Post Street and angle Sampson Street below Post Street is less than 900.
Answer: The angle formed by E Post Street and Sampson Street below Post Street is acute angle.
For #18 - #20, solve. Use u = 3.14 when necessary.
18) A water sprinkler sends water out in a circular pattern. The radius of watering is 6 feet. Determine how large an area is watered. Write your answer in complete sentence form and include correct units.
Solution:
Answer: The Area of the circular pattern is 113.04 feet2.
19) An airplane flying due south is 300 miles from the airport. Another airplane flying due west is 325 miles from the airport. How far apart are the two airplanes? Round to the nearest mile. Write your answer in complete sentence form and include correct units.
Solution:
Airplane flying due south is 300 miles from the airport and airplane flying due west is 325 miles.
It makes an angle of 900 at the airport.
