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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.
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Consider a triangle ABC like the one below. Suppose that C=83°, a = 43, and b = 44. Solve-example-1
User Pasquale
by
7.8k points

2 Answers

6 votes

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

User Sam Texas
by
7.1k points
2 votes

Answer:

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

User Kamranicus
by
7.0k points