warm up april 14th
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Warm Up April 14th. What is the hypotenuse if the leg lengths are a = 6 and b = 4? Simplify . EOCT Week 13 #1. Solve for x . 45. x. 3. 3. Solve for x . 45. 3√2. x. X=3. Solve for x . 45. 3. x. 3=x√2. Special Right Triangles. - PowerPoint PPT PresentationTRANSCRIPT
Warm Up April 14th1. What is the hypotenuse if
the leg lengths are a = 6 and b = 4?
2. Simplify
EOCT Week 13 #1
3
3
x
Solve for x
3 2x
45
x
3√245
Solve for x
X=3
x
345
Solve for x
3=x√22
3
223
22
23
You will be able to find the lengths of sides of special
right triangles30-60-90
And45-45-90
45-45-90 Right Triangle
x
x
2x
45
45
30-60-90 Right Triangle
a2a
30
60
a 330 : 60 : 90
a : a 3 : 2a
The longer leg is _____ times bigger than the shorter leg. The hypotenuse is _____ times bigger than the shorter leg.The longer leg is √3 times bigger
The hypotenuse is 2 times bigger than the shorter leg
Find the values of x and y. Give your answers in simplest
radical form.
Hypotenuse = 2(shorter leg)22 = 2xDivide both sides by 2.11 = x
Substitute 11 for x.
Just Watch
60
30
x
y
20
#1 You Try!
20=2x (hypotenuse is twice as big as shorter leg)
10=xY=x√3 (long leg is √3 times bigger than shorter leg)
Y=10√3
Find the values of x and y. Give your answers in simplest radical form.
Hypotenuse = 2(shorter leg)
Divide both sides by 2.
y = 27 Substitute for x.
#2 You Try!
Find the values of x and y. Give your answers in simplest radical
form.
Rationalize the denominator.
Hypotenuse = 2(shorter leg).
Simplify.
y = 2x
Just Watch
y60
30
x 21
#1 You Try!
21=x√3 (long side is √3 larger than short side) X= 21/√3……21√3/3……..7√3Y=2x (hypotenuse is twice as big as short side) Y=2(7√3)Y=14√3
Find the values of x and y. Give your answers in simplest radical
form.
Rationalize the denominator.
Hypotenuse = 2(shorter leg)x = 2y
Simplify.
#2 You Try!
Find the values of x and y. Give your answers in simplest radical form.
Simplify.
y = 2(5)y = 10
Just Watch
60
30x
y7
You Try!
X=7√3 (Long leg is √3 times larger than short side) Y=2(7) (Hypotenuse is twice as big as the short side) Y=14
Find the values of the variables. Give your answers in simplest radical form.
1. 2.
3. 4.
x = 10; y = 20
SPECIAL TRIANGLES SUMMARY
Finding an angle.(Figuring out which ratio to use
and an inverse trig button.)
111 tancossin
Ex: 1 Figure out which ratio to use. Find x. Round to the nearest tenth.
20 m
40 m
20tan40
26.6o
1 20tan40
x
Tan-1 20 / 40 )
Shrink yourself down and stand where the angle is.
Now, figure out which trig ratio you have and set up the problem.
x
Ex: 2 Figure out which ratio to use. Find x. Round to the nearest tenth.
15 m50 m 15sin
50
17.5 o
1 15sin50
x
Sin-1 15 / 50 )
Shrink yourself down and stand where the angle is.
Now, figure out which trig ratio you have and set up the problem.
x
Ex. 3: Find . Round to the nearest degree.
9
17.29
2.17tan
62
1 17.2tan 9
Ex. 4: Find . Round to the nearest degree.
23
7
237cos
72
1 7cos 23
When we are trying to find a side we use sin, cos, or tan.
When we are trying to find an angle we use
(INVERSE) sin-1, cos-1, or tan-1.