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3 years ago

Find x. Round your answer to the nearest tenth of a degree.

Mathematics

2 answers:

77julia77 [94]3 years ago

8 0

This is the concept of trigonometry, the value of x will be calculated as follows;
sin theta=[opposite]/[hypotenuse]
theta=x
opposite=16 units
hypotenuse=21 units
thus;
sin x=16/21
hence;
x=arcsin(16/21)
x=49.63
x=50 (to the nearest degrees)

svp [43]3 years ago

4 0

Answer: $x=49.6^{\circ}$

Step-by-step explanation:

In the given figure , we have right triangle with hypotenuse 21 units and the side opposite to angle x is 16 units.

According to the trigonometry,

$\sin \theta = \dfrac{\text{side opposite of }\theta}{\text{Hypotenuse}}$

So for , the given figure , we have

$\sin x = \dfrac{16}{21}\\\\\Rightarrow\ \sin x\approx0.7619\\\\\Rightarrow\ x=\sin^{-1}(0.7619)=0.8662\text{ radian}$ (using sine calculation)

Convert radian into degrees , we have

$x=0.8662\times\dfrac{180^{\circ}}{\pi}\\\\=0.8662\times\dfrac{180^{\circ}}{3.14159}=49.6319852107\approx49.6^{\circ}$ [Round to the nearest tenth.]

Hence, $x=49.6^{\circ}$

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Complete chart

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