Question

Fill in the blank. In the triangle below, x = ___. Round your answer to two
decimal places.

Answer 1

The correct answer is 37.53

Answer 2

x ≈ 37.53

Explanation:

To find the value of x, we will follow the steps below:

first, we need to find angle z

z+47° +90° = 180° (sum of interior angle of a triangle)

z + 137° = 180°

subtract 137° from both-side of the equation

Z + 137°-137° = 180° - 137°

Z=43°

angle Z = 43°

We can now use the sine rule to find the value of x

Using the sine rule

`(sin Z)/(z) = (sin X)/(x)`

where Z and X are angles and z and x are side length

from the diagram given,

X = 47° and we find Z to be 43°

side z = 35

we can now proceed to substitute the values into the formula

`(sin 43)/(35)` =
`(sin 47)/(x)`

cross-multiply

x sin 43° = 35 sin 47°

divide both-side of the equation by sin 43°

x sin 43° /sin 43°= 35 sin 47° /sin 43°

x ≈ 37.53 to two decimal place