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PythagorasPythagorasSpecialSpecialRightRight
TrianglesTriangles
The TangentThe TangentRatioRatio
The SineThe Sine& Cosine& Cosine
RatiosRatios
WordWordProblemsProblems
44
1313
xx
The value of x is thisThe value of x is this
What isWhat is
3√17 3√17
What is 6√5What is 6√5
a²+b²>c² a²+b²>c² is this type of triangle is this type of triangle
(classified by its angles)(classified by its angles)
What is acuteWhat is acute
This theorem This theorem states that if states that if
a²+b²=c²,a²+b²=c², then the then the triangle is a right triangle is a right
triangle.triangle.
What is the What is the Converse of Converse of
the the Pythagorean Pythagorean
TheoremTheorem
3,4,5 & 5,12,13 3,4,5 & 5,12,13 are examples are examples
of these.of these.
What is a What is a PythagoreaPythagorea
n Triplen Triple
This is the value This is the value of xof x
55
45°45° 45°45°
xx
What isWhat is5√25√2
44
60°60°
30°30°
xx
This is the value of xThis is the value of x
What isWhat is88
77
60°60°
30°30°
xx
This is the value of xThis is the value of x
What isWhat is7√37√3
7760°60°
30°30°
xx
This is the value of xThis is the value of x
What isWhat is7/2 or 3.57/2 or 3.5
7760°60°
30°30°xx
This is the value of xThis is the value of x
What isWhat is
(7√3)/2(7√3)/2
This is the Definition ofThis is the Definition ofThe Tangent RatioThe Tangent Ratio
What is What is opp/adjopp/adj
1111
77
ƟƟ
This is value of tanThis is value of tanƟƟ
What is What is 7/117/11
1111
77
ƟƟ
This is value of tanThis is value of tanƟƟ
What is What is 11/711/7
22
ƟƟ
55
This is the value of ƟThis is the value of Ɵ
What isWhat is22°22°
22
23°23°
xx
This is the value of xThis is the value of x
What isWhat is4.724.72
This is the This is the definition of Sinedefinition of Sine
What isWhat isopp/hypopp/hyp
This is the definition This is the definition of Cosineof Cosine
What isWhat isadj/hypadj/hyp
77
1212
ƟƟ
This is the sinThis is the sinƟƟ
What isWhat is7/127/12
The value of sin49The value of sin49
What isWhat is.7547.7547
77
1515
ƟƟ
Determine the value of ƟDetermine the value of Ɵ
What isWhat is28°28°
You are standing near the You are standing near the Washington monument which is Washington monument which is
555 ft tall. The angle of 555 ft tall. The angle of elevation from your position to elevation from your position to the top of the monument is 37°. the top of the monument is 37°.
How far are you from the How far are you from the monument?monument?
What is 736.5 ft
The angle of elevation from The angle of elevation from the base to the top of a the base to the top of a
water slide is about 28°. water slide is about 28°. The horizontal length of The horizontal length of
the slide is about 45 ft. Find the slide is about 45 ft. Find the height of the slide.the height of the slide.
What isWhat is23.9 ft23.9 ft
You lean a 20 ft ladder You lean a 20 ft ladder against a wall. The against a wall. The
base of the ladder is 4 base of the ladder is 4 ft from the wall. What ft from the wall. What
angle Ɵ does the angle Ɵ does the ladder make with the ladder make with the
ground?ground?
What isWhat is78°78°
A chair lift on a ski slope A chair lift on a ski slope has an angle of elevation has an angle of elevation of 28° and covers a total of 28° and covers a total distance of 2000 ft. To distance of 2000 ft. To
the nearest ft, what is the the nearest ft, what is the vertical height covered vertical height covered
by the chair lift?by the chair lift?
What is What is 1063.4 ft1063.4 ft
You are designing a You are designing a ramp where the ramp where the
horizontal distance is horizontal distance is twice as long as the twice as long as the
vertical rise. What will vertical rise. What will be the ramp angle to the be the ramp angle to the
nearest tenth of a nearest tenth of a degree?degree?
What isWhat is27°27°