SOLUTION: Hi Thank you for helping me out today. I am currently in Geometry in high school. I have learned Pythagorean Theorem before but I am struggling with square roots. I am given a ri

Question 957333: Hi Thank you for helping me out today. I am currently in Geometry in high school. I have learned Pythagorean Theorem before but I am struggling with square roots.
I am given a right triangle with a 30 degree angle also. The bottom line is 7sqrt3 and the Hypotenuse is labelled "w". The thirty degree angle is where the Hypotenuse and the bottom line connect. Could you please tell me the length of the hypotenuse? I want to say the answer is 14. Thank you so much!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
I am given a right triangle with a 30 degree angle also. The bottom line is 7sqrt3 and the Hypotenuse is labelled "w". The thirty degree angle is where the Hypotenuse and the bottom line connect. Could you please tell me the length of the hypotenuse? I want to say the answer is 14. Thank you so much!
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Since you have a 30-60 degree right triangle,
the side opposite the 30 degree angle is (1/2)
the length of the hypotenuse.
------
Sketch the triangle.
Let the side opposite the 30 degree angle be "x"
Then the hypotenuse is "2x"
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Use Pythagoras to solve for x and 2x.
----
x^2 + (7sqrt(3)]^2 = (2x)^2
----
x^2 + 49*3 = 4x^2
----
3x^2 = 147
x^2 = 49
x = 7
------
Hypotenuse = 2x = 14
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Cheers,
Stan H.
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