Precalculus Examples
SideAngleb=4c=a=A=B=45C=90SideAngleb=4c=a=A=B=45C=90
Step 1
The sine of an angle is equal to the ratio of the opposite side to the hypotenuse.
sin(B)=opphypsin(B)=opphyp
Step 2
Substitute the name of each side into the definition of the sine function.
sin(B)=bcsin(B)=bc
Step 3
Set up the equation to solve for the hypotenuse, in this case cc.
c=bsin(B)c=bsin(B)
Step 4
Substitute the values of each variable into the formula for sine.
c=4sin(45)c=4sin(45)
Step 5
Multiply the numerator by the reciprocal of the denominator.
c=4(2√2)c=4(2√2)
Step 6
Multiply 2√22√2 by √2√2√2√2.
c=4(2√2⋅√2√2)c=4(2√2⋅√2√2)
Step 7
Step 7.1
Multiply 2√22√2 by √2√2√2√2.
c=4(2√2√2√2)c=4(2√2√2√2)
Step 7.2
Raise √2√2 to the power of 11.
c=4(2√2√2√2)c=4(2√2√2√2)
Step 7.3
Raise √2√2 to the power of 11.
c=4(2√2√2√2)c=4(2√2√2√2)
Step 7.4
Use the power rule aman=am+naman=am+n to combine exponents.
c=4(2√2√21+1)c=4(2√2√21+1)
Step 7.5
Add 11 and 11.
c=4(2√2√22)c=4(2√2√22)
Step 7.6
Rewrite √22√22 as 22.
Step 7.6.1
Use n√ax=axnn√ax=axn to rewrite √2√2 as 212212.
c=4(2√2(212)2)c=4⎛⎜
⎜⎝2√2(212)2⎞⎟
⎟⎠
Step 7.6.2
Apply the power rule and multiply exponents, (am)n=amn(am)n=amn.
c=4(2√2212⋅2)c=4(2√2212⋅2)
Step 7.6.3
Combine 1212 and 22.
c=4(2√2222)c=4(2√2222)
Step 7.6.4
Cancel the common factor of 22.
Step 7.6.4.1
Cancel the common factor.
c=4(2√2222)c=4⎛⎝2√2222⎞⎠
Step 7.6.4.2
Rewrite the expression.
c=4(2√22)c=4(2√22)
c=4(2√22)c=4(2√22)
Step 7.6.5
Evaluate the exponent.
c=4(2√22)c=4(2√22)
c=4(2√22)c=4(2√22)
c=4(2√22)c=4(2√22)
Step 8
Step 8.1
Factor 22 out of 44.
c=2(2)(2√22)c=2(2)(2√22)
Step 8.2
Cancel the common factor.
c=2⋅(2(2√22))c=2⋅(2(2√22))
Step 8.3
Rewrite the expression.
c=2(2√2)c=2(2√2)
c=2(2√2)c=2(2√2)
Step 9
Multiply 22 by 22.
c=4√2c=4√2
Step 10
The result can be shown in multiple forms.
Exact Form:
c=4√2c=4√2
Decimal Form:
c=5.65685424…c=5.65685424…