A triangle has sides A, B, and C. Sides A and B have lengths of 3 and 5, respectively. The angle between A and C is #(5pi)/8# and the angle between B and C is # (pi)/12#. What is the area of the triangle?

↳Redirected from "Suppose that I don't have a formula for #g(x)# but I know that #g(1) = 3# and #g'(x) = sqrt(x^2+15)# for all x. How do I use a linear approximation to estimate #g(0.9)# and #g(1.1)#?"
1 Answer
LM
Dec 20, 2016

#5.95# square units

Explanation:

#A_triangle = 1/2ab sin C#

the angle to take as #C# is the angle sandwiched between the #2# given sides.

angle sandwiched between A and B = #pi -( 5pi)/8 - pi/12#

#=(24pi)/24 - (15pi)/24 - (2pi)/24#

#=(7pi)/24#

#A_triangle = (3*5)/2 * sin((7pi)/24)#

#= 7.5sin((7pi)/24)#

#=5.95# square units

(NB: when using #pi# as a measurement of angles, use the #Rad# setting on your calculator)

Related questions
See all questions in Area of a Triangle
Impact of this question
1506 views around the world
You can reuse this answer
Creative Commons License