Q: If $$\triangle ABC$$ has $$b = 270.5$$, $$c = 334.6$$, and $$\angle A = 42.8^\circ$$, what is the area of the triangle to the nearest whole number?

$$\dfrac{1}{2}bc \sin A = \dfrac{1}{2} \times 270.5 \times 334.6 \times \sin 42.8^\circ$$

Question 1

Given the triangle shown, suppose $$\angle C = 42.8^\circ$$, $$\angle A = 37.2^\circ$$, and $$b = 270.5. $$What is the measure of $$\angle B to $$the nearest tenth of a degree?

Accepted Answer

$$\angle B = 180^\circ - 42.8^\circ - 37.2^\circ = 100.0^\circ$$

Question 2

If in the triangle above, $$b = 270.5$$, $$c = 334.6$$, and $$\angle B = 37.2^\circ$$, use the Law of Sines to find the length of side $$a to $$the nearest tenth.

Accepted Answer

$$a = \dfrac{b \sin C}{\sin B} = \dfrac{270.5 \sin 42.8^\circ}{\sin 37.2^\circ}$$

Question 3

Which law should be used to solve for the unknown sides and angles in the triangle above if you are given two sides and the included angle?

Accepted Answer

Law of Cosines

Question 4

Suppose $$b = 270.5$$, $$c = 334.6$$, and $$\angle A = 42.8^\circ. $$Use the Law of Cosines to find the length of side $$a to $$the nearest tenth.

Accepted Answer

$$a^2$$ = $$b^2$$ + $$c^2 - 2bc$$ \cos A$$

Question 5

If $$	riangle ABC$$ has $$b = 270.5$$, $$c = 334.6$$, and $$\angle A = 42.8^\circ$$, what is the area of the triangle to the nearest whole number?

Accepted Answer

$$\dfrac{1}{2}bc \sin A = \dfrac{1}{2} 	imes 270.5 	imes 334.6 	imes \sin 42.8^\circ$$

Question 6

Given $$	riangle ABC$$ with $$b = 270.5$$, $$c = 334.6$$, and $$\angle B = 37.2^\circ$$, which formula would you use to find $$\angle C$$?

Accepted Answer

$$\angle C = 180^\circ - \angle A - \angle B$$

Question 7

If $$	riangle ABC$$ has $$b = 270.5$$, $$c = 334.6$$, and $$\angle B = 37.2^\circ$$, which of the following is the correct Law of Sines equation to solve for $$\angle C$$?

Accepted Answer

$$\dfrac{\sin B}{b} = \dfrac{\sin C}{c}$$

Question 8

A surveyor measures $$b = 270.5$$ meters and $$c = 334.6$$ meters from a point $$A$$ and finds the angle between them to be $$42.8^\circ. $$What is the most appropriate method to find the distance $$a$$ between the other two points?

Accepted Answer

Use the Law of Cosines

Question 9

If $$	riangle ABC$$ has $$b = 270.5$$, $$c = 334.6$$, and $$\angle A = 42.8^\circ$$, which of the following is the correct Law of Cosines equation for $$a$$?

Accepted Answer

$$a^2$$ = $$b^2$$ + $$c^2 - 2bc$$ \cos A$$

Question 10

Suppose you are given $$b = 270.5$$, $$c = 334.6$$, and $$\angle B = 37.2^\circ. $$Which step should you perform first to solve for $$\angle C$$?

Accepted Answer

Calculate $$\angle C$$ using the Law of Sines

Solving a Triangle Given a Side and Angle

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