Example 4

Jan 21, 2013

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Example 4

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EXAMPLE 4

You are skiing on a mountain with an altitude of 1200 meters. The angle of depression is 21 o . About how far do you ski down the mountain? EXAMPLE 4 Find a hypotenuse using an angle of depression SKIING = opp hyp 1200 = x x sin 21 o 1200. x = sin 21 o 1200. x 0.3584 ANSWER

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EXAMPLE 4

EXAMPLE 4. Find the volume of an oblique cylinder. Find the volume of the oblique cylinder. SOLUTION. Cavalieri’s Principle allows you to use Theorem 12.7 to find the volume of the oblique cylinder. V = π r 2 h. Formula for volume of a cylinder. = π(4 2 )(7). Substitute known values.

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EXAMPLE 4

You are designing a logo to sell daffodils. Use the information given. Determine whether m EBA = m DBC . Equation. Explanation. Reason. m ∠ 1 = m ∠ 3. m EBA = m 3+ m 2. m EBA = m 1+ m 2. Substitute m 1 for m 3 . EXAMPLE 4. Use properties of equality.

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EXAMPLE 4

2. Verify the identity = sin q . 1. –. =. 2. 2. 2. 2. 2. 2. 2. sec q – 1. sec q. sec q. sec q – 1. sec q . sec q. sec q. 2. 1. = 1 – ( ). sec q. 2. = 1 – cos q . 2. = s in q . EXAMPLE 4. Verify a trigonometric identity.

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example 4

example 4. Loan Repayment. Chapter 4.3. A business property is purchased with a promise to pay off a $60,000 loan plus the $16,500 interest on this loan by making 60 monthly payments of $1275. The amount of money remaining to be paid on the loan plus interest is given by the function

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EXAMPLE 4

Dice. When two six-sided dice are rolled, there are 36 possible outcomes, as shown. Find the probability of the given event. The sum is not 6. The sum is less than or equal to 9. EXAMPLE 4. Find probabilities of complements. P ( sum is not 6). = 1 – P ( sum is 6). 5. = 1 –. 36.

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EXAMPLE 4

Maps. Use a metric ruler and the map of Ohio to estimate the distance between Cleveland and Cincinnati. SOLUTION. From the map’s scale, 1 centimeter represents 85 kilometers. On the map, the distance between Cleveland and Cincinnati is about 4.2 centimeters. Use the scale on a map.

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EXAMPLE 4

Because TPQ and QPR form a linear pair, the sum of their measures is 180. ANSWER. The correct answer is B. EXAMPLE 4. Standardized Test Practice. SOLUTION. Because TPQ and QPR form a linear pair, the sum of their measures is 180°. The correct answer is B.

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EXAMPLE 4

A (–3, 1) , B (–1, 3) , C (1, 3) , D (3, 1). m AOC = m BOD = 90°. EXAMPLE 4. Identify a rotation. Graph AB and CD . Tell whether CD is a rotation of AB about the origin. If so, give the angle and direction of rotation. This is a 90° clockwise rotation.

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EXAMPLE 4

STEP 1. Write the prime factorization of each expression. 12 a 3 = 2 2 3 a a a. 9 a 2 = 3 3 a a. EXAMPLE 4. Finding the GCF of Monomials. Find the greatest common factor of 12 a 3 and 9 a 2. STEP 2. Find the common factors, 3 and a 2 . The GCF is their product. ANSWER.

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EXAMPLE 4

Trapeze. The photograph shows some of the angles formed by the ropes in a trapeze apparatus. Identify the congruent angles. If m DEG = 157° , what is m GKL ?. SOLUTION. There are two pairs of congruent angles:. DEF JKL and DEG GKL.

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EXAMPLE 4

The photograph shows some of the angles formed by the ropes in a trapeze apparatus. Identify the congruent angles. If m DEG = 157° , what is m GKL ?. SOLUTION. There are two pairs of congruent angles:. DEF JKL and DEG GKL.

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EXAMPLE 4

In the diagram of C, QR = ST = 16 . Find CU. Chords QR and ST are congruent, so by Theorem 10.6 they are equidistant from C . Therefore, CU = CV. EXAMPLE 4. Use Theorem 10.6. SOLUTION. CU = CV. Use Theorem 10.6. 2 x = 5 x – 9. Substitute. Solve for x. x = 3.

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EXAMPLE 4

Place an isosceles right triangle in a coordinate plane. Then find the length of the hypotenuse and the coordinates of its midpoint M. SOLUTION.

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EXAMPLE 4

Shopping Mall.

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EXAMPLE 4

SCULPTURE: The sculpture on the right is drawn on a graph where units are measured in inches. What is the approximate length of SR , the depth of a seat?. EXAMPLE 4. Find the distance between two parallel lines. 120 – 110. 10. 2. 110 – 80. 30. 3. –. –. =. =. =. =.

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EXAMPLE 4

In the diagram, N is the incenter of ABC . Find ND. By the Concurrency of Angle Bisectors of a Triangle Theorem, the incenter N is equidistant from the sides of ABC . So, to find ND , you can find NF in NAF . Use the Pythagorean Theorem stated on page 18. EXAMPLE 4.

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EXAMPLE 4

Some ice sculptures are made by filling a mold with water and then freezing it. You are making such an ice sculpture for a school dance. It is to be shaped like a pyramid with a height that is 1 foot greater than the length of each side of its square base. The volume of

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EXAMPLE 4

EXAMPLE 4. Solve a multi-step problem. SHOPPING. A discount shoe store is having a sale, as described in the advertisement shown. • Use the information in the ad to write a system of inequalities for the regular footwear prices and possible sale prices.

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EXAMPLE 4

log (4 x – 7) = log ( x + 5). 5. 5. Solve log (4 x – 7) = log ( x + 5). 5. 5. ANSWER. The solution is 4. EXAMPLE 4. Solve a logarithmic equation. SOLUTION. Write original equation. 4 x – 7 = x + 5. Property of equality for logarithmic equations. 3 x – 7 = 5.

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EXAMPLE 4

EXAMPLE 4. Solve a multi-step problem. COLLECTOR CAR. The owner of a 1953 Hudson Hornet convertible sold the car at an auction. The owner bought it in 1984 when its value was $11,000. The value of the car increased at a rate of 6.9% per year. a.

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EXAMPLE 4

Maps. The scale of the map at the right is 1 inch : 26 miles . Find the actual distance from Pocahontas to Algona. EXAMPLE 4. Use a scale drawing. SOLUTION. Use a ruler. The distance from Pocahontas to Algona on the map is about 1.25 inches . Let x be the actual distance in miles.

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