Asked by admin @ in Mathematics viewed by 298 People
Solve for the missing length and the other two angles in the triangle below.
Part 1 - use law of cosines to find the missing 3rd side
Part 2- use either the law of cosines or the law of sines to find the measure of angle C
Part 3- Use any method you like to find the measure of angle B
Answered by admin @
The triangle is missing, so i have attached it.
Answer:
1) 3rd side = 12.92
2)angle C = 82°
3)angle B = 44°
Step-by-step explanation:
1) To find the missing 3rd side which is opposite to angle A, using cosine rule, we have
a² = b² + c² - 2bc•cosA
From the image,
b = 7.4 and c = 15.8 while A = 54°
Thus,plugging in relevant values ;
a² = 7.4² + 15.8² - 2(7.4*15.8)•cos54
a² = 54.76 + 249.64 - 137.45
a² = 166.95
a = √166.95
a ≈ 12.92
2) Using sine rule, we can find angle C.
Thus,
a/sinA = c/sinC
So, sin C = (c*sinA)/a
c = 15.8
a = 12.92
A = 54°
Plugging in the relevant values;
sin C = (15.8*sin54)/12.92
sin C = 0.98936
C = sin^(-1)0.98936
C ≈ 82°
3) to get angle B, we know that sum of angles in a triangle = 180.
Thus,
A + B + C = 180
So,54 + B + 82 = 180
B + 136 = 180
B = 180 - 136
B = 44°
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