Question

Find the value of x and the value of y.
a.
x = 33.9
y = 32.8
c.
x = 17.0
y = 32.8
b.
x = 33.9
y = 98.4
d.
x = 17.0
y = 98.4

Answer 1

I know it's either A or B, I am just having trouble finding the y.

Answer 2

We can setup 2 simultaneous equations:

We form the first equation by using the cosine rule:
\[y^2 = x^2 + 24^2 - 2(x)(24)\cos105^{0}--------(1)\]
We form the second equation by taking the sum of the bases of the 2 small triangles.



We could use Pythagoras Theorem to find a.
\[x^2 = a^2+a^2\]
\[a=\sqrt{\frac{ 1 }{ 2 }x^2}\]

We could use the Sine Rule to find b.
\[\frac{ \sin90^0 }{ 24 }=\frac{ \sin60^0 }{ b}\]
\[b=\frac{ 24\sqrt3 }{ 2 }=12\sqrt3\]
\[y=a+b\]
\[y=\sqrt{\frac{ 1 }{ 2 }x^2}+12\sqrt3----------(2)\]

Solve (1) and (2) simultaneously to yield values of x and y.

Answer 3

Thank you