Unit #8 Review Right Triangle Trigonometry. 1. Which of the following could represent the sides of a right triangle?

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1 Name: Date: Unit #8 Review Right Triangle Trigonometry 1. Which of the following could represent the sides of a right triangle? (1) { 6, 8,14 } (2) {, 20, } (3) { 15, 20, } (4) {,15, 20 } 2. Which of the following sets could represent the sides of a right triangle? (1) { 4,,10 } (2) { 10, 24, 26 } (3) { 2, 5, 6 } (4) { 16, 20, 22 } 3. Which of the following represents the height of an equilateral triangle whose sides have lengths of 8 units? (1) 8 (2) 8 2 (3) 4 3 (4) Simone traveled 4 miles due East of his home and then an additional miles due North in order to get to her school. What is the shortest distance from Simone s house to her school rounded to the nearest tenth of a mile? (1) 11. (2) 8.1 (3) 6.4 (4). 5. Given the triangle shown below, which of the following represents cos? (1) 24 (2) 24 (3) 24 (4) Given the triangle below, which of the following represents tan S? (1) 5 (2) 5 (3) (4) 5 S 5 R lgebra 1, Unit Reviews, Unit # Right Triangle Trigonometry The rlington lgebra Project, LaGrangeville, NY 540

2 4. If sin = then which of the following is closest to the measure of angle? 5 (1) 53 (2) (3) 4 (4) 8 8. If cos D = 0. then the measure of angle D, to the nearest whole number, is (1) 28 (2) 83 (3) 65 (4) 41. Given the right triangle shown below, which of the following expressions would give the length of side? (1) ta n( 42 ) (3) (2) sin( 42 ) (4) cos( 42 ) sin ( 42 ) Given the right triangle shown below, which of the following expressions would calculate the length of side E? (1) t an 68 (3) tan 68 (2) cos 68 (4) cos 68 E 68 D 11. Which of the following represents the length of side RS to the nearest tenth? S (1) 42.6 (3) (2) 16.3 (4) 8.4 R. Which of the following represents, to the nearest degree, the measure of angle in right triangle shown below? (1) 22 (3) 44 (2) 35 (4) 46 lgebra 1, Unit Reviews, Unit # Right Triangle Trigonometry The rlington lgebra Project, LaGrangeville, NY 540

3 Part II nswer all questions in this part. Each correct answer will receive 2 credits. learly indicate. ladder that is 16 feet long leans against a building such that its base is feet from the bottom of the building. Draw a picture illustrating this scenario and determine, to the nearest tenth of a foot, how high up the building the ladder reaches. 14. ladder that is 16 feet long leans against a building such that it makes an angle of 60 with respect to the ground. Determine the height, h, that the ladder reaches up the side of the building accurate to the nearest tenth of a foot. [2 points] 16 feet h Thomas is trying to determine if a 15-foot long ladder will reach a roof that is twelve feet above the ground safely. The guidelines on the ladder claim that it will be safe as long as the angle it makes with respect to the ground is less than 65. Will Thomas s ladder safely reach the window feet above the ground? 15 feet lgebra 1, Unit Reviews, Unit # Right Triangle Trigonometry The rlington lgebra Project, LaGrangeville, NY 540

4 Part III - nswer all questions in this part. Each correct answer will receive 3 credits. learly indicate 16. tree casts a shadow that is 45 feet long at a time when the sun is at an angle of elevation of 35. Draw a picture of this scenario and determine the height of the tree to the nearest tenth of a foot. 1. In right triangle shown below, Maria measured the length of side as 6 inches and the length of side as 10 inches. She then used a protractor to measure angle and found it to be 42. Did Maria correctly measure the two sides and the one angle of this triangle? Justify your response. 10 inches 6 inches 42 Part IV - nswer all questions in this part. Each correct answer will receive 4 credits. learly indicate 18. Two people standing on a level road spot a hot-air balloon hovering 0 feet overhead. The person at point sees the balloon at an angle of elevation of 36, while the person at point sees the balloon at an angle of elevation of 52. Determine, to the nearest foot, the distance between the two people. 0 feet lgebra 1, Unit Reviews, Unit # Right Triangle Trigonometry The rlington lgebra Project, LaGrangeville, NY

5 1. boat is sailing dangerously towards a rocky shore as shown in the picture below. The boat knows that the height of the lighthouse is 40 feet. The angle of elevation when the boat was at point was 36 and the angle of elevation when it reached point was 48. Determine the distance the boat traveled from point to point to the nearest foot. [4 points] 40 feet helicopter is flying above two cars at a height of 0 feet. The angles of depression to the two cars are 35 and 62 respectively. Determine the distance that separates the two cars to the nearest foot. [4 points] ft 21. Evin is flying a kite such that the string is at an angle of elevation of 2. Initially, she lets 35 ft of string out and the kite rests at point. The wind begins to blow and she lets out an additional 20 feet of string resulting with the kite at point. How much higher is the kite at point then it was at point? Round your answer to the nearest tenth of a foot. 20 ft 35 ft lgebra 1, Unit Reviews, Unit # Right Triangle Trigonometry The rlington lgebra Project, LaGrangeville, NY 540 2

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