Question

What is the approximate value of x? Round to the nearest tenth.

A) 3.1 cm
B) 3.9 cm
C) 4.6 cm
D) 5.4 cm

Answer 1

option C is correct

The approximate value of x is, 4.6 cm(nearest to tenth)

Explanation:

In the given figure; the triangle is right angle triangle:

Label the figure:

then, the triangle XYZ is right angle triangle.

Using trigonometric ratio:

The ratio of the opposite side of a right triangle to the hypotenuse is called the sine. i.e,

`Sine=(opposite)/(Hypotenuse)`

using sine ratio in triangle XYZ:

`\sin 50^(\circ) = (XY)/(XZ)`

Substitute the value of XY = x cm and XZ = 6 cm in above ratio:

`\sin 50^(\circ) = (x)/(6)` or

`0.76604444247801 = (x)/(6)`

Simplify:

`x= 4.59626665` cm

Therefore, the approximate value of x nearest to tenth is, 4.6 cm

Answer 2

x = 6cm * sin(50) = 4.59

rounded to 4.6

Answer is C