Make sure you understand the concepts and procedures in this lesson by answering the questions below. The questions are similar to ones that you will see on the lesson quiz. Read any feedback carefully, and review this lesson if you answer any of the problems incorrectly and don't understand why.
Find the measure of angle C.
- 38°
- 40°
- 42°
- 44°
Use the Law of Cosines to solve for C.
c2 = a2 + b2 - 2abcos(C)
112 = 172 + 102 - 2(17)(10)cos(C)
121 = 289 + 100 - 340cos(C)
121 = 389 - 340cos(C)
-268 = -340cos(C)
.788 ≈ cos(C)
C ≈ 38°
Use the Law of Cosines to solve for C.
c2 = a2 + b2 - 2abcos(C)
112 = 172 + 102 - 2(17)(10)cos(C)
121 = 289 + 100 - 340cos(C)
121 = 389 - 340cos(C)
-268 = -340cos(C)
.788 ≈ cos(C)
C ≈ 38°
Use the Law of Cosines to solve for C.
c2 = a2 + b2 - 2abcos(C)
112 = 172 + 102 - 2(17)(10)cos(C)
121 = 289 + 100 - 340cos(C)
121 = 389 - 340cos(C)
-268 = -340cos(C)
.788 ≈ cos(C)
C ≈ 38°
Use the Law of Cosines to solve for C.
c2 = a2 + b2 - 2abcos(C)
112 = 172 + 102 - 2(17)(10)cos(C)
121 = 289 + 100 - 340cos(C)
121 = 389 - 340cos(C)
-268 = -340cos(C)
.788 ≈ cos(C)
C ≈ 38°
Find the measure of angle A.
- 111°
- 110°
- 109°
- 108°
Use the Law of Cosines to solve for A.
a2 = b2 + c2 - 2bccos(A)
172 = 102 + 112 - 2(10)(11)cos(A)
289 = 100 + 121 - 220cos(A)
289 = 221 - 220cos(A)
68 = 220cos(A)
-.309 ≈ cos(A)
A ≈ 108°
Use the Law of Cosines to solve for A.
a2 = b2 + c2 - 2bccos(A)
172 = 102 + 112 - 2(10)(11)cos(A)
289 = 100 + 121 - 220cos(A)
289 = 221 - 220cos(A)
68 = 220cos(A)
-.309 ≈ cos(A)
A ≈ 108°
Use the Law of Cosines to solve for A.
a2 = b2 + c2 - 2bccos(A)
172 = 102 + 112 - 2(10)(11)cos(A)
289 = 100 + 121 - 220cos(A)
289 = 221 - 220cos(A)
68 = 220cos(A)
-.309 ≈ cos(A)
A ≈ 108°
Use the Law of Cosines to solve for A.
a2 = b2 + c2 - 2bccos(A)
172 = 102 + 112 - 2(10)(11)cos(A)
289 = 100 + 121 - 220cos(A)
289 = 221 - 220cos(A)
68 = 220cos(A)
-.309 ≈ cos(A)
A ≈ 108°
Find side b.
- 47.1
- 48.2
- 49.1
- 50.5
Use the Law of Cosines to solve for side b.
b2 = a2 + c2 - 2accos(B)
b2 = 312 + 222 - 2(31)(22)cos(135°)
b2 = 961 + 484 - 1364(-.707)
b2 ≈ 2409.5
b ≈ 49.1
Use the Law of Cosines to solve for side b.
b2 = a2 + c2 - 2accos(B)
b2 = 312 + 222 - 2(31)(22)cos(135°)
b2 = 961 + 484 - 1364(-.707)
b2 ≈ 2409.5
b ≈ 49.1
Use the Law of Cosines to solve for side b.
b2 = a2 + c2 - 2accos(B)
b2 = 312 + 222 - 2(31)(22)cos(135°)
b2 = 961 + 484 - 1364(-.707)
b2 ≈ 2409.5
b ≈ 49.1
Use the Law of Cosines to solve for side b.
b2 = a2 + c2 - 2accos(B)
b2 = 312 + 222 - 2(31)(22)cos(135°)
b2 = 961 + 484 - 1364(-.707)
b2 ≈ 2409.5
b ≈ 49.1
Find side c.
- 14.7 m
- 14.2 m
- 15.5 m
- 19.9 m
Use the Law of Cosines to solve for c.
c2 = a2 + b2 - 2abcos(C)
c2 = 222 + 172 - 2(22)(17)cos(42°)
c2 = 484 + 289 - 748(.743)
c2 ≈ 217.236
c ≈ 14.7 m
Use the Law of Cosines to solve for c.
c2 = a2 + b2 - 2abcos(C)
c2 = 222 + 172 - 2(22)(17)cos(42°)
c2 = 484 + 289 - 748(.743)
c2 ≈ 217.236
c ≈ 14.7 m
Use the Law of Cosines to solve for c.
c2 = a2 + b2 - 2abcos(C)
c2 = 222 + 172 - 2(22)(17)cos(42°)
c2 = 484 + 289 - 748(.743)
c2 ≈ 217.236
c ≈ 14.7 m
Use the Law of Cosines to solve for c.
c2 = a2 + b2 - 2abcos(C)
c2 = 222 + 172 - 2(22)(17)cos(42°)
c2 = 484 + 289 - 748(.743)
c2 ≈ 217.236
c ≈ 14.7 m
Find angle C.
- 48.5°
- 46.7°
- 45.3°
- 44.6°
Use the Law of Cosines to find the measure of angle C.
c2 = a2 + b2 - 2abcos(C)
142 = 172 + 192 - 2(17)(19)cos(C)
196 = 289 + 361 - 646cos(C)
196 = 650 - 646cos(C)
-454 = -646cos(C)
cos(C) ≈ .703
C ≈ 45.3°
Use the Law of Cosines to find the measure of angle C.
c2 = a2 + b2 - 2abcos(C)
142 = 172 + 192 - 2(17)(19)cos(C)
196 = 289 + 361 - 646cos(C)
196 = 650 - 646cos(C)
-454 = -646cos(C)
cos(C) ≈ .703
C ≈ 45.3°
Use the Law of Cosines to find the measure of angle C.
c2 = a2 + b2 - 2abcos(C)
142 = 172 + 192 - 2(17)(19)cos(C)
196 = 289 + 361 - 646cos(C)
196 = 650 - 646cos(C)
-454 = -646cos(C)
cos(C) ≈ .703
C ≈ 45.3°
Use the Law of Cosines to find the measure of angle C.
c2 = a2 + b2 - 2abcos(C)
142 = 172 + 192 - 2(17)(19)cos(C)
196 = 289 + 361 - 646cos(C)
196 = 650 - 646cos(C)
-454 = -646cos(C)
cos(C) ≈ .703
C ≈ 45.3°
Find angle B.
- 75°
- 76°
- 77°
- 78°
Use the Law of Cosines to find the measure of angle B.
b2 = a2 + c2 - 2accos(B)
192 = 172 + 142 - 2(17)(14)cos(B)
361 = 289 + 196 - 476cos(B)
361 = 485 - 476cos(B)
-124 = -476cos(B)
.261 ≈ cos(B)
B ≈ 75°
Use the Law of Cosines to find the measure of angle B.
b2 = a2 + c2 - 2accos(B)
192 = 172 + 142 - 2(17)(14)cos(B)
361 = 289 + 196 - 476cos(B)
361 = 485 - 476cos(B)
-124 = -476cos(B)
.261 ≈ cos(B)
B ≈ 75°
Use the Law of Cosines to find the measure of angle B.
b2 = a2 + c2 - 2accos(B)
192 = 172 + 142 - 2(17)(14)cos(B)
361 = 289 + 196 - 476cos(B)
361 = 485 - 476cos(B)
-124 = -476cos(B)
.261 ≈ cos(B)
B ≈ 75°
Use the Law of Cosines to find the measure of angle B.
b2 = a2 + c2 - 2accos(B)
192 = 172 + 142 - 2(17)(14)cos(B)
361 = 289 + 196 - 476cos(B)
361 = 485 - 476cos(B)
-124 = -476cos(B)
.261 ≈ cos(B)
B ≈ 75°
Summary
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