Find the area of a triangle

Question

Determine the area of the triangle specified by a=7 ft, A=78°, and B=52°

Answer 1

 

h = 7sin(52) ≈ 5.5161 ft

 

base  is found by first noting angle C is  180-A-B = 180-78-52 = 50

 

base/sin(50) = 7/sin(78) ==>  base ≈ 5.4821 ft

 

==

Area = (1/2)base*h   —> you can plug in the numbers.   

 

Answer 2

tan 52 = h/(7-x)

tan 12 = x/h ---> x = h*tan 12


tan 52 = h/( 7 - h*tan12)

tan 52 * ( 7 - h*tan 12) = h

tan 52 * 7 - h * tan12*tan52 = h

tan 52 = h + h * tan 12*tan52

tan 52 = h ( 1+ tan12*tan52)

tan 52 / ( 1 + tan 12 * tan 52) = h

h = 1.0062

x = 1.0062 * tan 12 = 0.213873555

7-x = 6.78612645

 

As a check, arctan(h/x) = arctan(1.0062/0.213873555) = 78 

Area = 1/2 * 7 * 1.0062 = 3.5217