Question

What are the values of the variables in the triangle below? if the answer is not an integer, leave it in simplest radical form. the diagram is not drawn to scale

Answer 1

b.
`x=69,\ y=23√(3)`

Explanation:

The diagram shows the right triangle with an acute angle of
`30^(\circ).`

In
`30^(\circ)-60^(\circ)-90^(\circ)` right triangle, the leg opposite to the
`30^(\circ)` angle is half the hypotenuse, so

`y=(1)/(2)\cdot 46√(3)=23√(3)`

By the Pythagorean theorem,

`x^2+y^2=(46√(3))^2\\ \\x^2=(46√(3))^2-(23√(3))^2\\ \\x^2=46^2\cdot 3-23^2\cdot 3=23^2\cdot 3(4-1)\\ \\x^2=23^2\cdot 3^2\\ \\x=23\cdot 3=69`