Pencil highlighter red pen GP NB textbook homework
Pencil, highlighter, red pen, GP NB, textbook, homework If a jet climbs at an angle of 8 , what is the minimum distance between its take-off point & a 120 foot tower, so the jet will clear the tower by at least 50 feet? 50 ft 120 ft ? ? ? +2 8 x 170 ft tan 8 = 170 +1 x= 170 tan 8 x 1209. 61 ft +1 +1 The plane needs to start at least 1209. 61 ft away.
Look forof a pattern inare theshown first three figures. Draw T-61 a) What kind triangles in the pictures below? figures 4 & 5, and solve for of these the hypotenuse Wethe willlength refer to Isosceles Rightfigure Triangles in the last drawn. Fill in the table s. and then state as 45 -90 your observations. 2 1 1 3 2 Fig. # 1 Length of legs 1 unit 2 2 units 3 3 units 4 4 units 5 5 units n n units 5 4 3 4 5 Length of hypotenuse units In a 45 -90 , the hypotenuse is always times longer than the legs.
T-62 Here is another way to understand the isosceles right triangle relationship… a) Draw in one diagonal & shade in one of the right triangles formed. b) Label the angle measures in the other right triangle. 45 90 x 45 x c) If one leg has a length of x, what is the length of the other leg? Why? The other leg also has a length of x, since the sides of a square always equal by definition. d) What is the length of the hypotenuse in terms of x? (Use the Pythagorean Theorem & write in simple radical form. ) (Pythagorean Thm. )
2 30 60 1 4 30 60 2 6 hypotenuse is twice the length of the short leg. The long leg is times the short leg. b=? 8 10 60 3 60 Fig. Short # leg 1 1 unit In a 30 -60 -90 , the c=? 30 Below are what we refer to as 30 -60 -90 s. 30 T-63 4 n 60 “short “long leg”: leg 5 30 . opposite the 60 . Long hypotenuse leg units 2 2 units 4 units 3 3 units 6 units 4 4 units 8 units 5 5 units 10 units n n units 2 n units
a) Draw in a height & shade in one of the right triangles formed. b) Label the angle measures in the other right triangle. Here is another way to understand the 30 -60 -90 triangle relationship… 30 T-64 2 x 60 90 x c) If the hypotenuse has a length of 2 x, what is the length of the short leg? Why? The short leg has a length of x, since the height of an equilateral triangle bisects the base. (We proved this in T-52!!) d) What is the length of the long leg in terms of x? (Use the Pythagorean Theorem & write in simple radical form. ) (Pythagorean Thm. )
45 n 45 - 90 Triangle: Side ratio of 1: 1: OR Legs: n Hypotenuse: n Why do we need to know these? ? ? n • They give EXACT answers. • You need them on the SAT test! 30 • They are quicker & more convenient than trig. 2 n 60 n 30 - 60 - 90 Triangle: Side ratio of 1: : 2 OR Short Leg: n Long Leg: n Hypotenuse: 2 n
Find the values for x and y in each triangle without using your calculator. (Give exact answers!) T-65 a) b) 30 x 45 8 8 y y 45 x 60 30 - 60 - 90 Triangle: 45 - 90 Triangle: Legs: n = 8 u Hypotenuse: n Short Leg: n = 4 u Long Leg: n = 4 u Hypotenuse: 2 n = 8 u 2 n = 8 2 2 n = 4 x = 4 u y = 4 = 8 x = 8 u u y = 8 u u
T-66 Find the perimeter of a square which has a diagonal of length 5. Show you obtained your answer. 45 - 90 Triangle: Legs: n = 5 u Hypotenuse: n n = 5 P = 4 n = 4(5) = 20 u
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