SOLUTION: A right triangle has a hypotenuse of 9 yards. If one of the angles is 3 degrees, what is the area of this triangle? Explain your work.

Algebra ->  Triangles -> SOLUTION: A right triangle has a hypotenuse of 9 yards. If one of the angles is 3 degrees, what is the area of this triangle? Explain your work.       Log On


   

Question 1194385: A right triangle has a hypotenuse of 9 yards. If one of the angles is 3 degrees, what is the area of this triangle? Explain your work.
Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

x = length of the horizontal leg
y = length of the vertical leg

Let's say the 3 degree angle is near the horizontal leg (x)
This makes side x adjacent to the reference angle 3 degrees.

cos(angle) = adjacent/hypotenuse
cos(3) = x/9
x = 9*cos(3)
x = 8.987666
This value is approximate
Make sure your calculator is in degree mode.

And we can say
sin(angle) = opposite/hypotenuse
sin(3) = y/9
y = 9*sin(3)
y = 0.471024
which is also approximate

Now we can compute the area of this right triangle
area = base*height/2
area = x*y/2
area = 8.987666*0.471024/2
area = 2.116703

Answer: Approximately 2.116703 square yards