30-60-90
45-45-90
45-45-90
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
Given sin x = 5/13, find cos x.
cos x = 12/13
Use rectangle JKLM. Suppose JN is 8, and m∠KJL is 34 degrees.
Find KM and m∠KLJ.
KM = 16
m∠KLJ = 56 degrees
Use rhombus EFGH. If EF is 5 and IF is 4. Find the length of EI and FH.
EI = 3
FH = 8
Use trapezoid ABCD. Let m∠C=38. Find m∠A and m∠B.
m∠A=38
m∠B=142
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
Given that tanθ = 5/12 , determine cosθ and sinθ.
cosθ=12/13
sinθ=5/13
Use parallelogram ABCD. Let BE = 3x − 7 and BD = 24. Solve for x.
x = 19/3
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
Use kite ABCD. Let m∠DEC=8x+10. Solve for x.
x = 10
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
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
Use rectangle JKLM. Suppose m∠KLM = 9x−9. Solve for x.
x = 9
Use square ABCD. If BE is 9, find the length of AC and the length of AD.
AC = 18
AD = 9√2
Use trapezoid ABCD. Let AC=20 and let DB=6x−16. Solve for x.
x = 6
Find the perimeter of a square who has a diagonal of length 4√2 cm.
16cm.
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
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
Use square ABCD. Suppose m∠CAB=4x+5. Solve for x.
x = 10
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
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
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
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
Use square ABCD. Let EB=3x−1 and let AC=22. Solve for x.
x = 4
AC = 33, BD = 33, and DC = 40