c 12 B. _ r.; = - 2 = T. .;Xplanation: 2) A 45 B. -xplanation: 5. s-,:; Student Name:

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1 USTestprep, Inc..USJ\~fflp naltic Geometr EOC Qui nswer Ke Geometr- (MCC9-12.G.SRT.6) Side Ratios In Right Triangles, (MCC9-12.G.SRT.7) Sine nd Cosine Of Complementar ngles 1) Student Name: Teacher Name: Keith Simmons Date: Score: c 12 B Determine the tangent of L. ) B).;planation: Solution: 12. The tangent of an acute angle of a right triangle is the opposite side divided b the adjacent side. 12 2) c 4 B Find the length of side C. ) --..{ B) - 2 ~ 2 -xplanation: _ r.; Let the hpotenuse of the triangle be equal to n- 2. n-'il =, n. s-,:; = - 2 = T ~p:/twww.usatestprep.com/modules/qui_factor/ke.php 1/6

2 USTestprep, Inc. 3) B 7 c For this right triangle shown, what is the sine of angle C? ) :1ii 7 B) :1ii.,jV 7 ~ To find the length of leg B, the Pthagorean Theorem should be used. The Pthagorean Theorem states that il + t} = 2. where a and bare the lengths of the legs of the right triangle, and cis the length of the hpotenuse. For this reason, il + 72 = 2, or il + 49 = 64, where a is the length of leg B. lf 49 is subtracted from both sides of the equation, and if the square root is then taken of both sides, a is found to be 1. lso, the sine of an angle equals the length of the leg opposite the angle divided b the length of hpotenuse, or length of opposite leg. Therefore, since the length of the hpotenuse is and the length of the leg opposite angle C length of hpotenuse.s -..jts, the sine of angle C is -V1 (. tl.tp:/twww.usatestprep.com/modules/qui_factorll<e.php 216

3 311/201 USTestprep, Inc. 4) 100 feet 10 feet tree that is 100 feet tall casts a shadow that is 10 feet long. Determine the angle at which the ras of the sun hit the ground, to the nearest degree. ) 31' 42' B) 34' 6' The solution is 34. We can use the inverse tangent ratio to determine the angle of elevation. ngle= tan- 1 ( 100 ) 10 ngle= 34' ) Find the measure of LC to the nearest degree. ) 20' B) 22' 2~ s s c 24' 66' The solution is 22'. We can use an of the inverse trig ratios to calculate the measure of angle C. For example, tan" 1 (. ) = mlc

4 USTestprep, Inc. 6) (- 7 The angle of depression from the top of a flag pole to a point on the ground is 30. If the point on the ground is 7 feet from the base of the flag pole, how tall is the pole to the nearest foot? ) 3 feet 3 feet B) 43 feet 106 feet The solution is 43 feet Because the triangle is right and has a 30 angle, we know that it is a triangle. Therefore, the Long Leg= short Leg( --./3 ). So, 7 = x--./3 x = about 4 3feet 7) The hpotenuse and one of the Legs of a right triangle form an angle that has a cosine of :Ji. What is the measure of the angle? 2 ) 30 degrees 60 degrees B) 4 degrees 90 degrees ( The cosine of an angle equals the Length of the Leg adjacent to the angle divided b the Length of the hpotenuse, or Length of adjacent Leg. Since the fraction -. 1 r:; can be simplified to ~ b multipling both the numerator and the denominator Length of hpotenuse -'42 2 b --.j2, the measure of the angle in degrees can be determined b finding a triangle for which the ratio of the Length of one of the Legs to the Length of the hpotenuse is 1: ~ triangle is such a triangle, and since each of the Legs makes a 4- degree angle with the hpotenuse, the angle in question measures 4 degrees. 4/6

5 ) USTestprep, Jnc B +1 c In the right triangle shown, what is the cosine of angle C? ) 12 B) Since the legs of the right triangle measure x + 1 and x+ 1, respectivel, and since the hpotenuse measures x+ 17, the Pthagorean Theorem can be used as follows: (x + 1) 2 + (x + 1) 2 = (x + 17)2. This equation becomes (x 2 + 2x + 1) + (xl + 30x + 22) = x2 + 34x + 29, which then becomes 2x2 + 32x = x2 + 34x When all the terms are moved to one side, the equation becomes x2-2x- 63 = 0, and when the left side of the equation is factored, it becomes (x- 9)(x + 7) = 0. t this point, it seems as if x can equal 9 or -7, but if xwere -7, one of the legs would have a negative length, and this is impossible. For this reason x equals 9, and the legs of the triangle measure 10 and 24, respectivel, while the hpotenuse measures 26. Since cosine is length of adjacent leg' the cosine of angle C is 24, or 12. tength of hpotenuse 26 9) Which trigonometric value is equal to cos 62? ) cos 2 sin 2 B) sec 2 tan 2 The solution is found b appling the definition of complementar trig functions: cos (&Theta)= sin (90 -& Theta) cos (6r) =sin (90-62 ) Therefore the solution is sin 2s. &6

6 3/11201 USTestprep, Inc. 10) (. Which propert can be justified using the ratios in triangle YZ? ) B) sin Z = ~ sin Y = cos (90 + Y) q cos Z = sin (90 - Z) sin Z t an Y =- cos Since cos 40 =sin S0 = Y., the answer is cos Z =sin (90 - Z). 11) 40" Which propert can be justified using the ratios in triangle YZ? ) cosy=~ cos Z = sin (90 - Y) B) sin Y = cos (90 - Y) sin Y t an Z =- cos Since sin S0 =cos 40 = Y., the answer is sin Y =cos (90 - Y). httpjinww.usatestprep.com/mocules/qui_factor/ke.php 616