Question

In this triangle, what is the value of x?

Enter your answer, rounded to the nearest tenth, in the box.

Answer 1

The value of x is 56.7 mm.

Explanation:

In a right angled triangle

`\sin\theta=(Perpendicular)/(Hypotenuse)=(Opposite)/(Hypotenuse)`

The given triangle is a right angled triangle with opposite sides 66 mm and hypotenuse 79mm.

`\sin x=(66)/(79)`

Taking sin⁻¹ on both the sides.

`\sin^(-1)(\sin x^(\circ))=\sin^(-1)((66)/(79))`

`x^(\circ)=\sin^(-1)(66)/(79)`

`x^(\circ)=56.66^(\circ)`

`x\approx 56.7`

Therefore the value of x is 56.7 mm.