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Trigonometry Final Exam: Unit 5 Name: Final Review Unit 5 Q1 Which of the following is equivalent to csc x? Q5 Luis is standing on a street in New York City looking at the top of the Empire State Building A 1 sec x B 1 tan x C (sin x )(cos x ) D 1 sin x with a 30◦ angle of elevation. He is 767.6 meters from the Empire State Building. How tall is the Q2 Eric is flying an airplane at an altitude of 2200 feet. He sees his house on the ground at a 45◦ angle of depression. What is Eric’s è Empire State Building? 30◦ 767.6 m horizontal distance from his house at this point? 45◦ 2200ft A 383.8 m C 664.8 m B 443.2 m D 1329.5 m Q6 Which of the following statements is true? A A 110ft C 1100ft B 220ft D 2200ft As the measure of an acute angle increases, the sine and cosine of the angle increase. B As the measure of an acute angle increases, the sine and cosine of the angle decrease. Q3 Which is the closest value of the adjacent-to- C hypotenuse ratio of a 45◦ angle? As the measure of an acute angle increases, the sine and tangent of the angle increase. D As the measure of an acute angle increases, the cosine and tangent of the angle decrease. 45◦ Q7 In the figure shown, cos P = 0.60. What is the length of PN? A 1.414 C 1 B 0.5 11 D 0.707 Q4 What is m ∠N to the N nearest degree? P 14 24 cm A 0.25 centimeter B 14.4 centimeter C 40 centimeter D 44 centimeter M Q N A P 4 16◦ [Page: 1 of 3] B 17◦ C 63◦ D 73◦ AY2015 Final Review Trigonometry Final Exam: Unit 5 Q8 A proposed wheelchair ramp is shown. What is the rise of the ramp to the nearest inch? Q11 Which of the following can be used to determine m∠ A? C B 4.5◦ 180 in A A 14 inches C 81 inches B 12 inches D 181 inches Q9 Which ratio has the same value as sec ∠ E G F E A sin−1 B cos−1 BC AC C sin−1 AC BC D sin−1 BC AC BC AC Q12 In the diagram shown, a 12-foot slide is attached to a swing set. The slide makes a 65◦ A cos ∠E C cos ∠G angle with the swing set. Which answer most B cot ∠E D csc ∠G closely represents the height of the slide? Q10 In the diagram shown, 65◦ m∠ B = 42◦ and 12 AB = 25 feet. Which equation can be used to ft ? calculate the value of x? A A 5.0 feet C 10.9 feet B 5.6 feet D 25.7 feet 25 ft x Q13 Which is the exact value of cot 60◦ ? 42◦ B C A B A x = 25(sin 42◦ ) x = 25(cos 42◦ ) [Page: 2 of 3] B C D x = 25(tan 42◦ ) x= C sin 42◦ 25 D √1 3 √ 3 1 √2 3 √ 3 2 AY2015 Final Review Trigonometry Final Exam: Unit 5 Q14 Use the triangle shown to determine which of the ratios has a value of √ 9 3 cm 18 cm 1 2. Q17 Use 4 ABC to answer the following. A b C a c 9 cm 60◦ B Using trigonometric ratios, name the ratio A sin 30 D csc 60 B cos 30 E cos 60 C tan 30 F sec 30 b c in two different ways. Q15 When the sun’s rays are at an angle of 39◦ , the distance from the top of Dakota’s head to the tip of her shadow is 77 inches. About how tall is Dakota? Round your answer to the nearest inch if necessary. 39◦ h 77 in. Q18 A painter leans a 12-foot ladder against a wall. The angle of elevation of the ladder is 55◦ . Determine the distance the ladder reaches up the wall to the nearest tenth. 5 Q16 What is the value of csc x, if sin x = 13 ? [Page: 3 of 3] AY2015 Final Review