Pythagorean Theorem
Mean Proportional
Special Right Triangles
Solving Triangles
Miscellaneous
100
What condition/s must be met in order to use the Pythagorean Theorem?
1) triangle must be a right triangle
2) 2 sides must be given
100
How many triangles are in the following figure? Name them.
3: ABD, BCD, ACB
100
Draw the reference triangles for the 45-45-90 and the 30-60-90 right triangles. Include all angle measures and sides lengths.
angles: 45-45-90
sides: 1-1-radical2
1's across from the 45, radical2 across from the right angle
angles: 30-60-90
sides: 1-2-radical3 (1 across from the 30, radical3 across from the 60, and 2 across from the right angle)
100
In Algebra, we could solve 2x=14 by doing the opposite of multiplying by 2, which is dividing. We would divide each side by 2, leaving the expression as x=7. What is the operation called in trigonometry that would do the similar thing but for the tangent function?
arctan, inverse tan, or tan-1
100
What are the trigonometric ratios of sine, cosine, and tangent?
sin = opp/hyp
cos = adj/hyp
tan = opp/adj
200
What is the equation for the Pythagorean Theorem? What part of the triangle does each variable represent?
a2+b2=c2
a/b are the legs
c is the hypotenuse
200
Solve for x.
x = 6
200
Solve for x and y.
x = 9
y = 9radical2
200
In right triangle ABC, angle B is 90 degrees. What does Sin(A) equal in terms of angle B?
Sin(A) = Cos(90-A)
200
The slope of a line equivalent to the__________the angle of elevation?
Tangent
300
If a triangle has leg lengths of 6 and 8, what is the length of hypotenuse?
5
(it's a Pythagorean triple!!)
300
Solve for x.
x = 3radical2
300
Solve for x and y
300
Find the measure of angle a to the nearest hundredth.
a = 49.4583981264....
So, a = 49.46 degrees
300
In a right triangle ABC, angle B is the right angle. What is the relationship between the other two angles (in terms of their trigonometric functions).
SinA = CosB
OR
CosA = SinB
OR
TanA = Tan1/B and Tan B = Tan1/A
400
We know that 3-4-5 is a Pythagorean Triple. Name one of the other two Pythagorean Triples that we learned in class.
5-12-13 OR 8-15-17
400
Solve for x.
x = 3
400
x = 8
y = 4
z = 4radical3
400
A foot ladder leans against a wall. The foot of the ladder is 7 feet from the wall.
a. Find the vertical distance from the ground to the point where the top of the ladder touches the wall. Round your answer to the nearest tenth.
b. Determine the measure of the angle formed by the ladder and the ground. Round your answer to the nearest degree.
a. 14.4 feet
b. 64 degrees
400
What is the true ratio of an American Dollar bill?
4radical3
500
Steve is mowing a rectangular lawn. He decides to mow along the border first. He starts at the shed and mows one of the longer sides (50 yards) and one of the shorter sides (20 yards), but then Steve realizes that he's close to being out of gas in his mower!!! So he attempts to drive back to the shed in the quickest route possible- a straight line. How long is that distance? Round your answer to the nearest hundredth. *hint: DRAW A PICTURE*
53.85 yards
500
Solve for x.
x = 8
500
Martin walks his dog on level ground in a straight line with the dog’s favorite tree. The angle of elevation from Martin’s present location to the top of a nearby telephone pole is 30 degrees. The angle of elevation from the base of the tree to the top of the telephone pole is 45 degrees. If the telephone pole is 42 feet tall, how far are Martin and his dog from the tree? Round to the nearest tenth.
30.7 feet
500
Scott, whose eye level is 1.5m above the ground, stands from a tree. The angle of elevation of a bird at the top of the tree is 36 degrees. How far above the ground is the bird? Round your answer to the nearest tenth of a meter.
23.3 m
*Be careful*
If you got, 21.8m for your answer you found the distance the bird is above his line of sight. You forgot to account for his height, of 1.5m, in your calculations.
500
Find length DE to the nearest hundredth using the Law of Sines.
DE = 17.98946...
DE = 17.99