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For the given right triangle, find the value x to the nearest tenth:​

For the given right triangle, find the value x to the nearest tenth:​-example-1
User Spaark
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Hello!

For this type of problem, we are given a right triangle, and my go-to for finding a side length with another given side length and an angle value would most likely be the law of sines.

The law of sines states that:


(a)/(sin(A))=(b)/(sin(B))

In the given triangle, the
a would be 45, and the opposite angle
71, would be the
A.

The same can be applied to the other side of the proportion.


x=b

The opposite angle of side
x can be found using the definition of the combined angle of a triangle.


90+71+B=180


B=19

So now we can set up our proportion.


(45)/(sin(71))=(x)/(sin(19))


x=sin(19)*(45)/(sin(71))

And we get that
x is around 15.5.

Hope this helps!

User Rexy
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