Question

where a and b are the lengths of two of the sides and C is the included angle. If Upper A equals 14 in squared commaa equals 8 in commab equals 7 in commaand C is an acute​ angle, what must C​ be? Give your answer in degrees to the nearest hundredth.

Answer 1

`C=40.01^0`

Explanation:

Area =14 Inch squared

a=8 Inch

b = 7 Inch

DEFINITION: An Included Angle is the angle in between two adjacent sides.

Given the lengths of two sides of a triangle and an included angle.

Area of the Triangle,
`A=(1)/(2)abSinC`

Substituting the given values:

`A=(1)/(2)abSinC\\14=(1)/(2)*8*7*SinC\\18=28*Sin C\\Sin C =(18)/(28)\\ C=arcsin ((18)/(28))=40.01^0`

Angle C is 40.01 degrees to the nearest hundredth.