You know how Soh Cah Toa applies to right triangles; you can assign the adjacent side = 4 and hypotenuse = 7
CosФ = (adjacent) / (hypotenuse)
Then with the Pythagorean theorem
4² + b² = 7²
16 + b² = 49
b² = 49 - 16
b² = 33
b = √(33)
So "b" is the opposite side.
SinФ = (opposite) / (hypotenuse) = √(33)/7
TanФ = (opposite) / (adjacent) = √(33)/4
It's a simultaneous equation:
Steps:
1.Number the equations..
a+b=77 -1
a-b=13 -2
2. Choose what variable you want to use. In this case I would use the "b". Since the signs in front of the "b's" are different, add the two equations together
a + b = 77
+ + +
a (-b) = 13
Which gives;
2a = 90
Then solve to find a:
2a=90
a= 90/2
a=45
3.Then plug the "a" value into any of the original equations to find the "b" value. I would use equation 1 since the all the variables are positive.
a + b = 77
(45) + b = 77
b=77-45
b=32
4.Solution
a=45
b=32
Answer:
Step-by-step explanation:
I believe the answer is 11ft
