Method 1:
The sides of a right-angle triangle are equal when the angle = 45°
[tex] a^2 = b^2 + c^2 \\ a^2 = (3 \sqrt{ 2 })^2 + (3 \sqrt{ 2 })^2 \\ a^2 = 9 \times 2 + 9 \times 2 \\ a^2 = 36 \\ a = \sqrt {36} = 6 [/tex]
Method 2:
(Optional)
Using TOA CAH SOH method
Where:
TOA is Tan θ = Opposite/Adjasent
CAH is Cos θ = Adjasent/Hypotenuse
SOH is Sin θ = Opposite/Hypotenuse
You have an angle of 45° and OPPOSITE the angle is a known length.
These are the 2 information we know.
We need to find the third information, which is the HYPOTENUSE.
Notice the capatialised words start with the letter O ans H?
Find in the TOA CAH SOH the corresponding letters, in this case SOH.
SOH is sin θ = opposite/hypotenuse
Simply substitude in the values and find the hypotenuse!
sin 45° = (3√2)/ hypotenuse
hypotenuse = (3√2) / sin 45° = 6
Answer is B.
And there you go! Both methods can be used and gives the same answer.
However the limitations to method 2 are:
1. It must be a right-angle triangle
2. An angle and a side must be given.
If you think method 2 is too confusing, stick to method 1.
Good luck!
