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Unformatted text preview: side—as an alternative to applying the Pythagorean Theorem. Example: In the triangle shown below, what is the value of x ? (A) 3 (B) 2 (C) (D) (E) Solution: The correct answer is (B). Since the figure shows a 45°45°90° triangle in which the length of one leg is known, you can easily apply either the sine or cosine function to determine the length of the hypotenuse. Applying the function sin45° =
2 opposite 2 2 , then solve for x: = ; 2x = 2 2 ; x = 2 . x hypotenuse 2 x 2 , set the value of this function equal to 2 32 2 52 3 22 Example: In the triangle shown below, what is the value of x ? (A) (B) (C) (D) (E)
53 3 3
10 3 23 32 Solution: The correct answer is (D). Since the figure shows a 30°60°90° triangle, you can easily apply either the sine or the cosine function to determine the length of either leg. Applying the function sin60° =
3 , set the value of this function equal to x opposite , then solve for x: 4 hypotenuse 2 3x = ; 2x = 4 3 ; x = 2 3 2 4 www.petersons.com 278 Chapter 16 Exercise 1
Work out each problem. Circle the letter that appears before your answer. 1. In the triangle shown below what is the value of x ? 4. What is the area of the triangle shown below? (A) (B) (C) (D) (E) 2. 32
72 2 5 33 42 (A) (B) (C) (D) (E) 5. 52 7.5
13 3 3 93 2 53 In the triangle shown below, what is the value of x ? (A) (B) (C) (D) (E) 3. 4 32 5 33
10 3 If two interior angles of a triangle measure 30° and 60°, and if the side of the triangle opposite the 60° angle is 6 units long, how many units long is the side opposite the 30° angle? (A) 3 (B) 2 3 (C) 4 (D) 3 2 (E)
53 2 Two trains depart at the same time from the same terminal, one traveling due north and the other due east, each along a straight track. If the trains travel at the same average speed, which of the following most closely approximates the number of miles each train has traveled when the shortest distance between the two trains is 70 miles? (A) 49 (B) 55 (C) 60 (D) 70 (E) 140 www.petersons.com Additional Geometry Topics, Data Analysis, and Probability...
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This note was uploaded on 08/15/2010 for the course MATH a4d4 taught by Professor Colon during the Spring '10 term at EmbryRiddle FL/AZ.
 Spring '10
 Colon
 SAT

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