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Sloan [31]
3 years ago
11

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

Mathematics
1 answer:
scZoUnD [109]3 years ago
3 0

Answer:

x ≈ 37.53

Step-by-step 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

\frac{sin Z}{z} = \frac{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

\frac{sin 43}{35}  = \frac{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

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