Question

solve the triangle. round lengths to the nearest tenth and angle measures to the nearest degree a=7 b=7 c=5

Answer 1

Hello,

a,b,c are the sides.

1) first idea
Theorem of Al' Kashi (genralized pythagorean theorem) will help us

a²=b²+c²-2bc cosA  ==>49=49+25-2*7*5*cos A
==>cos A=25/70=5/14 ==>
A=69,075167572361683699967605141899 °≈69°

b²=a²+c²-2ac cos B ==> 49=49+25-2*7*5 * cos B==>cos B=5/14
B=A (triangle is isocele ==> a second method)

C=180-2*69=42°

II)
The triangle isocele is formed with 2 right triangles.
(base=5/2 hypotenuse=7)

cos B=(5/2)/7=5/14 (the same) ==>B=69°
A=B=69°
C=42°