Question

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 1

D) 50.5°

Explanation:

got it right on edge :)

Answer 2

ANSWER


`x = 50.5 \degree`

EXPLANATION

We use the sine rule for solving triangles.

This is given by the formula,



`( \sin(A) )/(a) = ( \sin(B) )/(b) = ( \sin(C) )/(c)`


From the triangle,


`( \sin(x) )/(60) = ( \sin(40) )/(50)`

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


`sin(x) = ( 60\sin(40 \degree) )/(50)`



`sin(x) = 0.7713`



We solve for x to obtain,


`x = arcsin(0.7713)`



`x = 50.475`

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


`x = 50.5 \degree`