Find all missing sides/angles. Round each answer to the nearest unit.
Angles/sides ABC (left to right)
1) Angle c= 70 deg
side b= 28 yd
side c= 26 yd
2) Side a= 18 cm
Side b= 24 cm
Side c= 28 cm
sinB/b = sinC/c
that will get you B
Then A+B+C=180 gets you A
a^2 = b^2+c^2 - 2bc cosA
gets you A. Then,
b/sinB = c/sinC = a/sinA gets you A and B
To find missing sides/angles in a triangle, we can use various trigonometric ratios such as sine, cosine, and tangent. Let's solve the given problems step by step.
1) Angle c = 70 deg, side b = 28 yd, side c = 26 yd
To find the missing angles/sides, we can use the Law of Sines. The Law of Sines states that in a triangle:
a/sin(A) = b/sin(B) = c/sin(C)
Step 1: Find angle A
We have angle c = 70 deg and side c = 26 yd. Let's find angle A using the Law of Sines:
a/sin(A) = c/sin(C)
a/sin(A) = 26/sin(70)
a = sin(A) * 26 / sin(70)
a ≈ (sin(A) * 26) / 0.9397 ≈ 27.693
So, side a ≈ 27.693 yd
Step 2: Find angle B
We have side b = 28 yd. Using the Law of Sines:
a/sin(A) = b/sin(B)
27.693 / sin(A) = 28 / sin(B)
sin(B) = (28 * sin(A)) / (27.693)
B = arcsin((28 * sin(A)) / (27.693))
B ≈ arcsin((28 * 0.9397) / (27.693)) ≈ 61.75 deg
So, angle B ≈ 61.75 deg
2) Side a = 18 cm, side b = 24 cm, side c = 28 cm
To find the missing angles/sides, we can use the Law of Cosines. The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles.
Step 1: Find angle A
We have side b = 24 cm, side c = 28 cm, and side a = 18 cm. Let's find angle A using the Law of Cosines:
a² = b² + c² - 2bc * cos(A)
18² = 24² + 28² - 2 * 24 * 28 * cos(A)
324 = 576 + 784 - 1344 * cos(A)
Cos(A) = (576 + 784 - 324) / (1344) ≈ 1.419
A = arccos(1.419)
A ≈ 24.3 deg
So, angle A ≈ 24.3 deg
Step 2: Find angle B
We have side a = 18 cm and side c = 28 cm. Using the Law of Cosines:
cos(B) = (a² + c² - b²) / (2ac)
cos(B) = (18² + 28² - 24²) / (2 * 18 * 28)
cos(B) = (324 + 784 - 576) / (1008)
cos(B) = 532 / 1008 ≈ 0.528
B = arccos(0.528)
B ≈ 58.6 deg
So, angle B ≈ 58.6 deg
To summarize:
1) Angle A ≈ 24.3 deg, Angle B ≈ 61.75 deg, Side a ≈ 27.693 yd
2) Angle A ≈ 24.3 deg, Angle B ≈ 58.6 deg