The diagram below shows the dimensions of a triangular park built in a new housing development. Two side lengths and one angle measure are given.What is the measure of angle X? Round the answer to the nearest tenth.

ANSWER

[tex]x = 50.5 \degree[/tex]

EXPLANATION

We use the sine rule for solving triangles.

This is given by the formula,


[tex] \frac{ \sin(A) }{a} = \frac{ \sin(B) }{b} = \frac{ \sin(C) }{c} [/tex]


From the triangle,

[tex] \frac{ \sin(x) }{60} = \frac{ \sin(40) }{50} [/tex]

We multiply both sides of the equation by 60 to get,

[tex] sin(x) = \frac{ 60\sin(40 \degree) }{50} [/tex]


[tex] sin(x) = 0.7713[/tex]



We solve for x to obtain,

[tex] x = arcsin(0.7713)[/tex]


[tex] x = 50.475[/tex]

To the nearest tenth, we round to one decimal place to get,

[tex] x = 50.5 \degree[/tex]