Applications of Laws of Sines and Cosines

A surveyor at point S locates a rock formation 530 meters away at point P. The surveyor turns clockwise 102 degrees and locates ar ock formation 410 meters away at point R. To the nearest tenth of a meter, what is the distance between the rock formations?

x=___________

A stone wall makes an angle of 51 degrees with the side of your house that is 12 m long. You want to make a back yard play area for your dog by using 10 m of fencing to enclose a triangular region, as shown. At what distance from point C should the fencing be attached to the stone wall? Is there more than one possibility?

First, answer the question:

Is there more than one possibility? Yes or no, and why?

Evaluate responses using AI:

OFF

Evaluate responses using AI:

OFF

Now we know the two possible values for angle A are 68.84 degrees or 111.16 degrees. With that in mind, what are the two possibilities for the measure of angle B?

Evaluate responses using AI:

OFF

Which Law would you use?

• Law of Sines

• Law of Cosines

• Law of the Jungle

• Law of Gravity

Which Law would you use?

• Law of Sines

• Law of Cosines

• Law of the Jungle

• Law of Gravity

Use the Law of Sines to solve for side a.

Round your answer to the nearest hundredth.

Mathematical Equivalence

OFF

Find the length of side b.

Round your answer to the nearest hundredth.

Mathematical Equivalence

OFF

Which Law would you use? (a)  

• Law of Sines

• Law of Cosines

Use law of Sines to find side c.

Round your answer to the nearest hundredth

Mathematical Equivalence

OFF