a problem of trigonometry

Question

If θ = 60º and the side opposite θ  has length 299, how long is the hypotenuse? Give answer in exact form.

My answer is 299/root3 , but wrong.

Answer 1

Theta = 60 degrees

side opposite 60 is 299

side opposite 90 is the hypotenuse =h

use the Law of Sines

h/sin90 = h/1 = h = 299/sin60 = 299/(sqr3/2) = 598/sqr3 in exact form

or

= (598/3)sqr3 also in exact form,but with a rational denominator

= about 345.26

your answer 299/root3 was correct except for a factor of 2

2(299)/sqr3 = 598/sqr3 is correct

299/root3 is half the correct answer

299/root3 = about 172.6<299

the hypotenuse is the largest side, so it has to be larger than 299

299/sqr3 < 299 < 598/sqr3

172.6 < 299 < 345.3