Question

Consider a triangle ABC like the one below. Suppose that C=83°, a = 43, and b = 44. Solve the triangle.

Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth.
If there is more than one solution, use the button labeled "or".

Answer 1

The missing sides and angles are;

• c = 58
• A = 47 degrees
• B = 50 degrees

How do you solve a triangle?

When given certain information about a triangle, one must solve the triangle by determining its unknown sides and angles. The information given determines the methods for solving a triangle.

We have that;

`c^2` =
`a^2` +
`b^2` - 2abCosC

`c^2` =
`(43)^2` +
`(44)^2`- 2(43)(44)Cos83

`c^2` = 1849 + 1936 - 461

c = 58

Then;

a/Sin A = c/SinC

43/SinA = 58/Sin83

SinA = 43Sin83/58

= 0.7359

A = Sin-1( 0.7359)

= 47 degrees

B = 180 - (47 + 83)

B = 50 degrees

Answer 2

Step-by-step explanation:

In a triangle

a / sin A = b / sinB = c / sinC

Putting the values

43 / sin A = 44 / sinB

sinA / sinB = 43 / 44 = 1 / 1.023

A + B = 180 - 83 = 97

sinA / sin ( 97 - A ) = 1 / 1.023

sin 97 cos A - cos 97 sin A = 1.023 sin A

= .9925 cos A + .122 sin A = 1.023 sin A

.9925 cos A = .901 sin A

squaring

.985 cos²A = .8118 sin²A

.985 - .985 sin²A = .8118 sin²A

.985 = 1.7968 sin²A

sinA = .74

A = 47.73

B = 49.27

c / sin C = b / sin B

c = b sinC / sinB

= 44 x sin 83 / sin 49.27

= 44 x .9925 / .7578

= 57.62