SOLUTION: Two angles of a triangle measure 75� and 51�. The side opposite the largest angle measures 25 inches. How long is the shortest side?

Question 322449: Two angles of a triangle measure 75� and 51�. The side opposite the largest angle measures 25 inches. How long is the shortest side?
Answer by nyc_function(2741) (Show Source): You can put this solution on YOUR website!
I know that this is a geometry question but it can be solved using trigonometry.
We use the law of sines.
The sum of the angles of a triangle is 180 degrees.
To find the missing angle, add 51 + 75 and then subtract the sum from 180.
This will give you 54 degrees.
We now use the law of sines.
Let x = the missing side we want to find
sin51/x = sin75/25
x(sin75) = sin51(25)
x(sin75) = 19.42864904
x = 19.42864904/sin75
x = 20.11401756
The side opposite the smallest angle is 20 inches.

RELATED QUESTIONS
Two sides of triangle ABC measure 7.5 inches and 10 inches. One of the angles measures... (answered by stanbon)

The smallest angle of a triangle measures 44 degrees less than the largest angle. The sum (answered by shree840)

The measure of the largest angle of a triangle is 12 degree less than the sum of the... (answered by ankor@dixie-net.com)

the measure of the largest angle of a triangle is 45 degrees moe than the measure of the... (answered by checkley77)

The sides of a triangle measure 18 inches, 25 inches, and 36 inches. To the nearest... (answered by Alan3354)

The measures of the angles of a triangle are 50�, 35�, and 95�. What is the measure of... (answered by jim_thompson5910)

In a right triangle, angle A measures 20�. The side opposite angle A is 10 centimeters... (answered by ewatrrr)

In a right triangle, angle A measures 20�. The side opposite angle A is 10 centimeters... (answered by Alan3354)

i have a triangle with three angles of 45 75 and 60 degrees. the side opposite the 45... (answered by Theo)