Geometry Name _______________________
SG: Chapter 8: Right and Oblique Triangles Pd. ________ Date ____________
Complete each sentence with the word(s) that best completes each statement or phrase.
1. The Pythagorean Theorem can only be used with ___________________ triangles.
2. Triangles that are non-right are called ___________________ triangles.
3. A __________________________ is the comparison of two values
4. ___________________ is the trigonometric ratio that relates the side opposite your point of view and the side adjacent
your point of view in a triangle.
5. The branch of mathematics that involves triangle measurement is called____________________________ .
6. ______________ is the trigonometric ratio that relates the side opposite your point of view and the hypotenuse of a
7. A ________________________ is the equation stating that two ratios are equivalent.
8. The angle of ______________________ is the angle formed by the horizontal and the line of sight up to an object.
9. ______________________ is the trigonometric ratio that relates the side adjacent your point of view and the hypotenuse
of a triangle.
10. The angle of ______________________ is the angle formed by the horizontal and the line of sight down to an object.
11. To apply the Law of Cosines you must either be given all three side lengths or two sides and the ________________
12. To apply the Law of Sines you need an angle of the triangle and the side _____________________ that angle.
13. A common Pythagorean triple is _______ _______ _________.
14. In solving trigonometric ratios, if the variable is in the denominator you ______________________.
15. In solving trigonometric ratios, you utilize the inverse trig keys if you are solving for the _________.
16. In solving trigonometric ratios, if the variable is in the numerator you _________________.
17. The ________________________ is opposite the right angle in a triangle.
18. The two special types of right triangles are ____________________ and ___________________.
19. The _____________________________ and _____________________________ are the two methods
used to determine side and angle measurements in non-right triangles
20. An ______________________ right triangle has angle measurements of 45°-45°-90°.
21. The Greek symbol Ө is called ______________ and is used to represent an ____________ in the triangle.
22. Pythagorean Theorem can be used to solve for the ______________ or _____________ in a right triangle.
23. Trigonometric ratios, the Law of Sines, and the Law of Cosines can be used to solve for ___________ and _________ in
24. Capital letters used in the Law of Sines and Law of Cosine formulas represent ____________ of the triangle.
25. Lower case letters used in the Law of Sines and Cosines formulas represent ______________ of the triangle.
Multiple Choice Calculations- 4 points each no partial credit.
1. Find the perimeter of the triangle. A) 35 B) 49 C) 84 D) 98
2. Find the area of the triangle. A) 960 B) 48 C) 93 D) 480
3. Solve for x. 4. Solve for x.
A) 114.1 B) 174.3 C) 82.9 D) 102.4 A) 43.9 B) 137.4 C) 143.7 D) 12.3
141 x 42
5. Find the height of the trapezoid. 6. Solve for x.
A) 6.6 B) 8 C) 176 D) 288 A) 39.7 B) 18 C) 20.6 D) 22
10 10 26 30
7. Determine the perimeter of the triangle. 8. Determine the altitude of the triangle
A) 105 B) 111.8 C) 24.9 D) 42 A) 14.0 B) 26.3 C) 37.6 D) 11.3
9. If < C =28°, b = 7 and <A = 112°, find a. A) 5.1 B) 10.1 C) 40 D) 48
10. If < A = 105°, b = 8.4 and a =24, find <B. A) 55.2 B) 19.8 C) 20.4 D) 54.6
11. If < A = 104°, b = 8 and c = 12, find a. A) 29.2 B) 46.8 C) 8.9 D) 15.9
12. If a = 7, b = 12 and c= 16, find <A. A) 41.4 B) 44.0 C) 112.0 D) 23.9
13. The diagonal of a square is 15. Find the length of a side of the square
A) 8.7 B) 10.6 C) 21.2 D) 26.0
14. Determine the perimeter of an equilateral triangle with a height of 8 cm.
A) 83.1 cm B) 13.9 cm C) 27.7cm D) 41.6 cm
15. How high on a wall will a ladder reach if the ladder is 25 feet long and the base of the ladder is 7 feet from the
bottom of the building?
A) 24 square feet B) 26 square feet C) 24 feet D) 26 feet
16. A ski slope is 675 yards long with a vertical drop of 112 yards. Find the angle of depression of the slope.
A) 80.4° B) 80.6° C) 9.4° D) 9.6°
Calculations- 4 points each no partial credit. Points awarded on correct answer only.
17. Solve for each variable.
8 4 e
a b 12
18. In a right triangle, the measures of the legs are 7 and x + 8 and the measure of the hypotenuse is x + 9.
19. In triangle PQR, < Q = 90° and sin P = 9/41. Find all the missing parts of triangle PQR.
20. A ranger at the top of a look out tower spots a forest fire burning in the woods nearby. If the angle of elevation
from the fire to the ranger is 24° and the tower is 275 feet high. How far is the fire from the base of the tower?
Open Ended Calculations- 6 points each partial credit awarded.
ONLY CHOOSE 4 PROBLEMS TO COMPLETE
21. The perimeter of a rhombus is 36 inches and one of its angles equals 60°. Find the lengths of the diagonals.
22. A ship is sighted from two radar stations 147 km apart. The angle between the line segment joining the two
stations and the radar beam of the first station is 38°. The angle between the line segment joining the two
stations and the beam from the second station is 132°. How far is the ship from the second station?
23. The height, length and width of a rectangular box are 8, 9 and 12 respectively. Find the length of the
diagonal of the box. (3 dimensional)
24. Carol is in the Skydeck of the Sears Tower overlooking Lake Michigan. She sights two sailboats going due west
from the tower. The angles of depression to the two boats are 54° and 32°. If the sky deck is 1261 feet high how
far apart are the boats?
25. The waterway between Lake Huron and Lake Superior separates the United States and Canada at Sault Sainte
Marie. The railroad drawbridge located at the Sault Sainte Marie is normally 27 feet above the water when it is
closed. Each section of this drawbridge is 220 feet long. Suppose the angle of elevation of each section is 65°.
a) Find the distance from the top of a section of the drawbridge to the water.
b) Find the width of the gap created by the open drawbridge sections
26. A pilot must veer from her course to avoid a thunderstorm. Her course change consists of turning her plane 31°
to the north and flying 76 miles then making a second adjustment of 104° back toward her original course.
How many miles did she add to her course by making the detour?
27. The angle formed by the line of sight from Earth to Sirius and the line of sight from Earth to Alpha
Centuri is 68*. Earth to Sirius is 7.8 light- years and Earth to Alpha Centuri is 3.6 light-years.
Find the distance between Sirius and Alpha Centuri.