unit 7: right triangles and trigonometry

pythagorean theorem

100

what is the formula for pythagoream theorem 

a² + b² = c²

200

9² + 17² = x² 

what is x?

x = 19.2

300

what type of triangle is this? 

20, 21, 29

right

400

what type of triangle is this 

5, 9, 10

acute

500

what type of triangle is this 

3, 15, 18

not a triangle

special right triangles

100

what is the formula for 45-45-90 special right triangles?

leg=x

hypotenuse=x√ 2

200

what is the formula for 30-60-90 special right triangles?

short leg=x

long leg=x√ 3

hypotenuse=2x

300

30-60-90

what is the hypotenuse if the short leg is 9?

18

400

45-45-90

what is the legs if the hypotenuse is 16?

8√ 2

500

30-60-90

what is the long leg if the hypotenuse is 22?

11√ 3

similar right triangles & geometric mean

100

14 and 32 

8 square root 7 

200

6 and 40.5 

9 square root 3 

300

15 and 24 

6 square root 10

400

triangle- altitude x, long leg 20, short leg 9

6 square root 5 

500

triangle- hypotenuse 18, short part of hypotenuse leg 2, hypotenuse of bigger triangle (not whole triangle) 

72 square root 2 

trig & angle of elevation/depression

100

tan54=x/9

solve for x

12.4

200

sin46=24/x

solve fo x

33.4

300

cos35=x/21

solve for x

17.2

400

tan74=555/x

solve for x 

159.1 

500

tan-1(275/1324)

solve for x

11.7 degrees 

law of sines & law of cosines

100

What does SOHCAHTOA stand for 

Sine opposite over hypotenuse, cosine adjacent over hypotenuse, tangent opposite over adjacent 

200

sin119/x=sin27/5

solve for x

9.6

300

x²=22²+27²-2(22)(27)cos73

solve for x

29.4 

400

sin40/x=sin55/20

solve for x

15.7 

500

11²=10²+17²-2(17)(10)cosx

solve for x

38 degrees