Q: Suppose you are asked to find the area of the triangle using the given information. Which formula would you use?

$$\text{Area} = \frac{1}{2} ab \sin C$$

Question 1

Given the triangle in the image, with $$AB = 140 yd$$, $$BC = 160 yd$$, and $$	riangle ABC$$ with $$	riangle B = 80^\circ$$, what is the distance from $$A to$$ $$C (to $$the nearest yard)?

Accepted Answer

$$AC = 252 yd$$

Question 2

Which law is most appropriate to use to solve for $$AC in $$the triangle shown in the image?

Accepted Answer

Law of Cosines

Question 3

Using the Law of Cosines, which equation correctly represents the calculation for $$AC in $$the triangle?

Accepted Answer

$$AC^2$$ = $$140^2$$ + $$160^2 - 2(140)(160$$)\cos(80^\circ)$$

Question 4

After finding $$AC$$, which formula would you use to find angle $$A in $$the triangle?

Accepted Answer

$$\sin A = \frac{160 \sin 80^\circ}{AC}$$

Question 5

Suppose you are asked to find the area of the triangle using the given information. Which formula would you use?

Accepted Answer

$$	ext{Area} = \frac{1}{2} ab \sin C$$

Question 6

Calculate the area of the triangle to the nearest square yard.

Accepted Answer

$$13,770 yd$^2$$

Precalculus Study Guide: Trigonometric Identities, Angle Formulas, and Triangle Applications

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