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CW#77: Pythagorean, Special Right Triangles, Trig Geometry Name: ________________________________ TP: _______ CRS CLASS OF 2015 AVERAGE MASTERY PPF602: Use the Pythagorean Theorem 51% PPF601: Apply properties of 30-60-90, 45-45-90, similar, and congruent triangles 48% FUN 502 Express sine, cosine, and tangent of an angle in a right triangle as a ratio of given side lengths 46% FUN602: Apply basic trigonometric ratios to solve righttriangle problems. 56% HOW DO YOU STACK UP?! FISCHER MASON/YOUNG WALDEN/ZIEGLER 1ST X 57% X 3RD X 4TH X X 5TH 53% X 58% HOW DO WE STACK UP?! Campus Rauner Golder UIC Noble Muchin Percent Mastery 66% 63% 61% 58% 58% Place 1 2 3 4 4 YOU ALL TRYING TO BE FOURTH PLACE?! We didn’t think so… Get your TEAMS in gear… Get hyped… It’s time to PUSH IT TO THE LIMIT. You re-take the interim in ____ days. Today, I commit to: __________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ _______________________________________________________________________________________________________________________. PUSH IT TO THE LIMIT. INDEPENDENT REFLECTION: Write down everything you know about standard PPF602: Use Pythagorean Theoreom. Find the area of the triangle. Leave your answer in simplified radical form. 1) 2) Determine if the following triangles are right triangles. Triangles are right triangles if Pythagorean Theorem holds true. 4) 3) Sides: 3, 4, 5 5) The top of a ladder rests against a wall, 23 feet above the ground. The base of the ladder is 6 feet away from the wall. What is the length of the ladder? 6) In rectangle MNLO below, how much longer is the perimeter than the diagonal ML? M 24 m N 18 m O PUSH IT TO THE LIMIT. L 7) A rectangular field shown below is 60 feet wide and 40 feet long. Alissa and Bianca are at point B. Alissa walks to point C by walking along the edge of the field through point A. Bianca walks to point C by walking diagonally across the field. To the nearest whole, how many meters more does Alissa walk than Bianca? 8) One route along flat terrain from Madison to South Bend is to drive south from Madison for 400 miles to Chicago, then at Chicago to drive east 500 miles to South Bend. If a straight flat road existed between Madison and South Bend, how many miles would it be? Madison A B Chicago C South Bend D INDEPENDENT REFLECTION: Write down everything you know about standard PPF601: Apply properties of 30-60-90, 45-45-90, similar, and congruent triangles. 9) Find the value of each variable. Write answers in the simplest radical form. 10) Triangle CDE is a right triangle. The measure of CED is 45 degrees, and the length of CE is 22 inches. What is the length of CD? C D E 11) Triangle ABC is a right triangle. The measure of 12) What is the perimeter of the triangle below? ABC is 45 degrees, and the length of the hypotenuse is 6. What is the length of one of the legs? PUSH IT TO THE LIMIT. 13) In a 30-60-90, the shortest leg has a measure of 10 yards. What is the value of the perimeter? 14) In a 30-60-90 triangle, the hypotenuse has a measure of 20 inches. What is the value of the perimeter? INDEPENDENT REFLECTION. Write down everything you know about FUN 502 Express sine, cosine, and tangent of an angle in a right triangle as a ratio of given side lengths, and FUN602: Apply basic trigonometric ratios to solve right-triangle problems. 15) Find each trigonometric ratio for the given right triangle. A sin A = ______ b cos A = ______ tan A = ______ sin C = ______ c C B a 16) Find each trigonometric ratio for the given right triangle. sin A = ______ cos A = ______ tan A = ______ A 13 5 C B 12 sin B = _______ cos C = ______ cos B = ________ tan C = _______ tan B = _______ 17) An angle in a right triangle has a measure of β. 36 If tan β = 15 , then sin β = ? 18) An angle in a right triangle has a measure of Φ. 3 If cos Φ = 5 , what is sin Φ ? PUSH IT TO THE LIMIT. 19) An angle in a right triangle has a measure . If 8 tan = 15 , then sin = ? 20) An angle in a right triangle has a measure of 5 If sin = 13 , what is cos ? 21) In the figure below, ABC is a right triangle with a right angle at C. Which of the statements about this figure is NOT correct? Label sides A, O, H. 22) You are at the top of a roller coaster 100 feet above a. cos A = 3 5 . the ground. The angle of depression is 44°. What is the distance x? A 5 3 4 5 b. sin A = 3 c. tan A = 4 d. cos B = C 4 B 4 5 3 4 23) A lamppost if 11 feet tall. If the angle of elevation is 49 degrees. Which of the following is a trig ratio that could be used to find x? Solve for x. x A. sin 49 11 tan B = 24) A lamppost, shown below, casts a 10ft. shadow when the sun is at a 60° angle with the ground. Which of the following would give the height of the lamppost? What is the height to the nearest whole? tan 10 60 tan 60 B. 10 C. 60 tan 10 D. 10 tan 60 A. x B. cos 49 11 C. sin 11 49 x D. sin 49 11 x E. tan 49 11 x PUSH IT TO THE LIMIT. 25) To calculate the height h of a flagpole, you move 22 feet from the base and record the angle of elevation to the top to be 65°. Find the flagpole's height to the nearest foot. 26) A staircase has an angle of elevation of 28° and covers a total distance of 17ft. To the nearest foot, what is the vertical height h covered by the staircase? 27) The angle of elevation from the base to the top of a water slide is about 28°. The horizontal length of the slide is about 45 feet. Find the height h of the slide to the nearest whole. 28) You lean a 16 foot ladder against the wall. If the ladder makes an angle of 70° with the ground, how far away from the wall is the base of the ladder? Round your answer to the nearest tenth of a foot. 29) You are standing near the Washington Monument which is 555 feet tall. The angle of elevation from your position to the top of the monument is 45°. How far are you from the monument? 30) You are using a ladder to paint the side of a building. If you place the ladder 4 feet away from the wall, with an angle of elevation of 75.5 degrees. PUSH IT TO THE LIMIT. Name: _______________________________ TP: _____ EXIT SLIP Score: ______ / 2 1) 2) 3) Reflect in complete sentences. A) What do all of the standards we learned about today have in common? B) When do you use Pythagorean Theorem? C) When do you use trigonometric ratios (SOHCAHTOA)? PUSH IT TO THE LIMIT. CHALLENGE You are traveling along a stretch of highway that has a slight grade with an angle of inclination of 5°. After traveling for 4 miles, what is the vertical v and horizontal h change in feet? (1 mi = 5280 ft). Round your answer to the nearest foot. PUSH IT TO THE LIMIT.