13.1 – Use Trig with Right Triangles

Hypotenuse: Opposite side: Adjacent side: Side opposite right angle Hypotenuse Opposite  Side opposite reference angle Adjacent Side next to reference angle, not hypotenuse

opp hyp adj hyp opp adj sin  = cos  = tan  = hyp opp hyp adj adj Hypotenuse Opposite hyp opp hyp adj adj opp csc  = sec  = cot  =  Adjacent 1 . sin  1 . cos  1 . tan  csc  = sec  = cot  = csc = cosecant SOH – CAH – TOA sec = secant cot = cotangent

1. Evaluate the six trigonometric functions of the angle . c2 = a2 + b2 H O 152 = a2 + 92 225 = a2 + 81 144 = a2 12 = a 12 A 9 15 12 15 9 12 sin  = cos  = tan  = 15 9 15 12 12 9 csc  = sec  = cot  =

2. Let  be an acute angle of a right triangle 2. Let  be an acute angle of a right triangle. Find the value of the other five trigonometric functions of . c2 = a2 + b2 H O 52 = a2 + 42 5 4 25 = a2 + 16  9 = a2 3 A 3 = a 4 5 3 5 4 3 sin  = cos  = tan  = 5 4 5 3 3 4 csc  = sec  = cot  =

H O A c2 = a2 + b2 2 1 adj opp cot  = c2 = 1 + 3 c2 = 4 c = 2 4 5 3 5 2. Let  be an acute angle of a right triangle. Find the value of the other five trigonometric functions of . c2 = a2 + b2 H O 2 1 adj opp cot  = c2 = 1 + 3  c2 = 4 A c = 2 4 5 3 5 4 3 sin  = cos  = tan  = 5 4 5 3 3 4 csc  = sec  = cot  =

H O A c d c 7 d 7 sin 42° = cos 42° = 1 1 7  sin 42° = c 3. Find the measure of the missing sides. Round to the nearest hundredth. c d H O c 7 d 7 sin 42° = cos 42° = 1 1 7  sin 42° = c 7  cos 42° = d A 4.68 = c 5.20 = d SOH – CAH – TOA

H A O a b 14 a 14 b tan 57° = sin 57° = 1 1 a  tan 57° = 14 3. Find the measure of the missing sides. Round to the nearest hundredth. a b H A 14 a 14 b tan 57° = sin 57° = 1 1 O a  tan 57° = 14 b  sin 57° = 14 a = 9.09 16.69 = b SOH – CAH – TOA

H A O A = 40°, c = 8 A B C a b c 40° SOH – CAH – TOA 8 50° 90° 5.14 a 4. Solve ABC, using the diagram and the given measurements. A = 40°, c = 8 A B C a b c 40° SOH – CAH – TOA H 8 50° A 40° 90° O 5.14 a b 6.13 a 8 b 8 sin 40° = cos 40° = 8 1 1 8  sin 40° = a 8  cos 40° = b a = 5.14 6.13 = b

Remember special triangles? 45° 90° 30° 60° 90° 1 1 1 2 45° 60° 1 2 1 45° 30° 1

5. Find the exact values of the variables. 13 1 y = 1

5. Find the exact values of the variables. 1 x = 60° y = 14 2

5. Find the exact values of the variables. 3 1 y = 2

5. Find the exact values of the variables. 1 2 y =