Do Now Section 2 4 Solving Right Triangles

Do Now •

Section 2. 4 Solving Right Triangles Objective: SWBAT determine the number of significant digits in a number and solve a right triangle.

Significant Digits According to this definition,

Significant Digits The relationship between the accuracy of the sides of a triangle and the accuracy of the angles in the same triangle is shown in the table: • We are now ready to use the definition of significant digits to solve right triangles. We solve a right triangle by using the information given about it to find all of the missing sides and angles.

Solving a Triangle To solve a triangle means to find the measures of all the angles and sides of the triangle. When solving triangles, a labeled sketch is an important aid. Use a to represent the length of the side opposite angle A, b for the length of the side opposite angle B, and so on. In a right triangle, the letter c is reserved for the hypotenuse.

Solving Right Triangles Unless stated otherwise, we round our answers so that the number of significant digits in our answers matches the number of significant digits in the least significant number given in the original problem. Also, we round our answers only and not any of the numbers in the intermediate steps. Finally, we are showing the values of the trigonometric functions to four significant digits simply to avoid cluttering the page with long decimal numbers.

Solving a Right Triangle Given Two Sides In right triangle ABC, a = 2. 73 and b = 3. 41. Find the remaining side and angles. Solution: We can find A by using the formula for tan A. Now, to find A, we use a calculator.

Solving a Right Triangle Given Two Sides In right triangle ABC, a = 2. 73 and b = 3. 41. Find the remaining side and angles. Solution: Next we find B. Use the Pythagorean Theorem to find c

Solving a Right Triangle Given Two Sides Solve right triangle ABC if a = 11. 47 cm and c = 27. 82 cm. B a = 11. 47 C • B = 90 24. 35 B = 65. 65 c = 27. 82 A

Solving a Right Triangle Given Two Sides In right triangle ABC, if a = 29. 43 cm and c = 53. 58 cm. Solution: Use the Pythagorean Theorem to find b

SOLVING A RIGHT TRIANGLE GIVEN AN ANGLE & A SIDE Solve right triangle ABC, if A = 34° 30′ and c = 12. 7 in.

Solving a Right Triangle, Given an Angle & a Side Solve right triangle ABC, if A = 42 30' and c = 18. 4. • B = 90 42 30' B B = 47 30' c = 18. 4 42 30' C A

Homework • Page 73 -74 # 9 -14, 19 and 20