SOLUTION: solve the right triangle given that m < A=30degrees, m < C=90degrees, and a=15. round your result to one decimal place

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Question 1121779: solve the right triangle given that m < A=30degrees, m < C=90degrees, and a=15. round your result to one decimal place
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

the right triangle given that:
+m < A=30 degrees,
m < C=90 degrees, and
a=15
since the sum of all angles in triangle is 180, we have

m < B=+180-%2890%2B30%29
m < B=+180-120
m < B=+60%29 degrees
since m < A=30 degrees side and a=15 ,use sin theorem to calculate hypotenuse c
sin%2830%29=a%2Fc
1%2F2=15%2Fc
%281%2F2%29c=15
c=30

and, now use Pythagorean theorem to fond side b
b%5E2=c%5E2-a%5E2
b%5E2=30%5E2-15%5E2
b%5E2=900-225
b%5E2=675
b=sqrt%28675%29
b=25.98076211353316
or approximately
b=25.9


Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!
solve the right triangle given that m < A=30degrees, m < C=90degrees, and a=15. round your result to one decimal place
This is a "special" 30-60-90 right-triangle. 

With the shorter leg being 15 (opposite the smallest angle), and the triangle named ABC, the 

That's all!! Nothing more, nothing less!