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

ANSWER

$x = 50.5 \degree$

EXPLANATION

We use the sine rule for solving triangles.

This is given by the formula,


$\frac{ \sin(A) }{a} = \frac{ \sin(B) }{b} = \frac{ \sin(C) }{c}$


From the triangle,

$\frac{ \sin(x) }{60} = \frac{ \sin(40) }{50}$

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

$sin(x) = \frac{ 60\sin(40 \degree) }{50}$


$sin(x) = 0.7713$



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,

$x = 50.5 \degree$