Question

Please help with my homework

Solve the given triangles by finding the missing angle in the other side lengths.

Answer 1

Explanation:

`\angle \: A + \angle \: B + \angle \: C = 180 \degree \\ \therefore \: 18 \degree + \angle \: B + 140 \degree = 180 \degree \\ \therefore \: \angle \: B + 158 \degree = 180 \degree \\ \therefore \: \angle \: B = 180 \degree - 158 \degree \\ \huge \red{ \boxed{\therefore \: \angle \: B = 22 \degree}}`

Answer 2

The user @Hrishii is correct about the value of angle B.

Once you know all three angles, you can use the law of sines to find the missing sides.

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Let's use the law of sines to find side b

b/sin(B) = a/sin(A)

b/sin(22) = 1/sin(18)

b = sin(22)*1/sin(18)

b = 1.21225240111352

b = 1.21 rounding to two decimal places

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Repeat for side c

c/sin(C) = a/sin(A)

c/sin(140) = 1/sin(18)

c = sin(140)*1/sin(18)

c = 2.08010440004024

c = 2.08 rounding to two decimal places

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The fully solved triangle is

A = 18 degrees

B = 22 degrees

C = 140 degrees

a = 1

b = 1.21

c = 2.08

decimal values are approximate