Show:
30-60-90
45-45-90
Trig
Parallelogram and Rectangle
Square and Rhombus
Kite and Trapezoid
100

If the hypotenuse of a 45-45-90 triangle has a length of 6, what are the lengths of the other two sides? 

leg 1 = 3√2   

leg 2 = 3√2

100

Given sin x = 5/13, find cos x.

cos x = 12/13

100

Use rectangle JKLM. Suppose JN is 8, and m∠KJL is 34 degrees. 

Find KM and m∠KLJ. 

KM = 16

m∠KLJ = 56 degrees

100

Use rhombus EFGH. If EF is 5 and IF is 4. Find the length of EI and FH. 

EI = 3

FH = 8 

100

Use trapezoid ABCD. Let m∠C=38. Find m∠A and m∠B.


m∠A=38

m∠B=142

200

If the length of the short leg is 4 in a 30-60-90 triangle, what is the length of the longer leg and the length of a hypotenuse?

hypotenuse = 8 

longer leg = 4√3

200

Given that tanθ = 5/12 , determine cosθ and sinθ. 


cosθ=12/13

sinθ=5/13

200

Use parallelogram ABCD. Let BE = 3x − 7 and BD = 24. Solve for x. 


x = 19/3

200

Use rhombus EFGH. If m∠GEF = 65, find the m∠GEH, m∠EIH and m∠EHI. 

m∠GEH = 65

m∠EIH = 90

m∠EHI = 25

200

Use kite ABCD. Let m∠DEC=8x+10. Solve for x.


x = 10

300

If the length of the longer leg is 6 in a 30-60-90 triangle, what is the length of the shorter leg and the length of a hypotenuse?

shorter leg = 2√3

hypotenuse = 4√3

300

From a point 340 meters from the base of the Hoover Dam, the angle of elevation to the top of the dam is 33°. Find the height of the dam to the nearest meter.

220.8 meters

300

Use rectangle JKLM. Suppose m∠KLM = 9x−9. Solve for x.

x = 9

300

Use square ABCD. If BE is 9, find the length of AC and the length of AD. 

AC = 18 

AD = 9√2

300

Use trapezoid ABCD. Let AC=20 and let DB=6x−16. Solve for x. 


x = 6

400

Find the perimeter of a square who has a diagonal of length 4√2 cm.

16cm.

400

A 25ft ladder is leaning up against a wall. If the ladder makes a 63 degrees with the ground, how far is the base of the ladder from the wall?

11.3 ft

400

Use parallelogram ABCD. Suppose m∠D = x+15 and m∠A = 4x+25. Find the measure of angle D and A. 

m∠D = 43

m∠A =137

400

Use square ABCD. Suppose m∠CAB=4x+5. Solve for x. 


x = 10 

400

Use kite ABCD. Let AB = 4x+17, BC = 5x+13, and DC = 3x+14. Find the length of AB, BC and DC.

AB = 33, BC = 33, DC = 26

500

Your square bedroom has a diagonal of 9√2 feet.  What is the length of each side? What is the area of your bedroom?

length of each side: 9 ft

area: 81 ft2

500

From the top of a lighthouse 210 feet high, the angle of depression of a boat is 27 ̊. Find the distance from the boat to the foot of the lighthouse. The lighthouse is built at sea level.


412.2 ft

500

Plot the points below. Show that AB and DC are parallel and congruent, in order to prove the shape is a parallelogram. 

A (0,3) 

B (5,5) 

C (8,2)

D (3,0)

Slope of AB AND DC =2/5

Length of AB and DC = √29


500

Use square ABCD. Let EB=3x−1 and let AC=22. Solve for x. 


x = 4

500
Use trapezoid ABCD. Let AC = 2x+21, BD = 5x + 3 and DC = 4x+16. Find the length of AC, BD and DC.

AC = 33, BD = 33, and DC = 40