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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.

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 meas class=

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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]

likeafairy221b

Answer:

D) 50.5°

Step-by-step explanation:

got it right on edge :)

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