Real World Triangle Problems Triangle Techniques Law of

Real World Triangle Problems

Triangle Techniques Law of Cosines • Usually used to find the length of the third side of an SAS triangle • Can also be used to find an angle measure in an SSS triangle • You CAN’T use it if you only know one side Law of Sines • Usually used to find a side length on an ASA or AAS triangle • You CAN’T use it for SSS or SAS triangles Area Formulas • Used for SAS triangles Heron’s Formula • Used for SSS Triangles

Example 1 – Textbook Page 474 Problem #1 Mountain Height Problem: A surveying crew has the job of measuring the height of a mountain. (see figure in book) From a point on the level ground they measure an angle of elevation of 21. 60 to the top of the mountain. They move 507 m closer horizontally and find that the angle of elevation is now 35. 80. How high is the mountain?

Example 1 – Textbook Page 474 Problem #1 Mountain Height Problem: A surveying crew has the job of measuring the height of a mountain. (see figure in book) From a point on the level ground they measure an angle of elevation of 21. 60 to the top of the mountain. They move 507 m closer horizontally and find that the angle of elevation is now 35. 80. How high is the mountain? m . 99 8 120 21. 6 o 507 m 2 . 144 14. 2 o 445. 06 m o 35. 8 o

Example 2 – Textbook Page 474 Problem #2 Studio Problem: A contractor plans to build an artist’s studio with a roof that slopes differently on the two sides. (see figure in textbook) On one side, the roof makes an angle of 33 0 with the horizontal. On the other side, which has a window, the roof makes an angle of 65 0 with the horizontal. The walls of the studio are planned to be 22 ft apart. a) Calculate the lengths of the two parts of the roof. b) How many square feet will need to be painted for each triangular end of the roof?

Example 2 – Textbook Page 474 Problem #2 Studio Problem: A contractor plans to build an artist’s studio with a roof that slopes differently on the two sides. (see figure in textbook) On one side, the roof makes an angle of 330 with the horizontal. On the other side, which has a window, the roof makes an angle of 650 with the horizontal. The walls of the studio are planned to be 22 ft apart. a) Calculate the lengths of the two parts of the roof. 12. 1 ft 820 650 20. 1 ft 330 22 ft b) How many square feet will need to be painted for each triangular end of the roof? Find the area of the triangle! There are MANY ways this can be done since we know every angle and every side. Here is one way: A =. 5 bc. Sin. C =. 5(22)(12. 1)Sin 65 = 120. 63 square feet

Assignment RED BOOK Pages 528 -529 Problems 49 -67 odd