A triangle has sides 2.4 and 9.0 and the measure of the angle between those sides is 98°.98 degrees . What is the area of the triangle?
In ΔPQR,m∠P=85°,m∠R=54°,cap delta and QR=q r equals 30. What is PR?
In ΔHJK,m∠J=14°,HK=6,cap delta and JK=j k equals 11. What is m∠Hm angle h ?
Do you UNDERSTAND?
Vocabulary Suppose you are given information about a triangle according to SSS, SAS, AAS, and ASA. For which of these can you immediately use the Law of Sines to find one of the remaining measures?
Error Analysis Suppose you used the Law of Sines and wrote a=3sin22°sin45°.eh equals . fraction 3 sine , 22 degrees , over sine , 45 degrees end fraction . . Is that the same equation as a=3sin(2245)°?eh equals 3 sine . open , 22 over 45 , close . degrees . question mark Explain.
Practice and Problem-Solving Exercises
A Practice
Find the area of each triangle. Round your answer to the nearest tenth. See Problem 1.
Use the Law of Sines. Find the measure x to the nearest tenth. See Problems 2 and 3.
In ΔDEF,m∠F=43°,d=16cap delta mm, and f=24f equals 24 mm. Find m∠D.m angle d .
In ΔABC,m∠A=52°,c=10cap delta ft, and a=15ft.eh equals 15 , ft. Find m∠C.m angle c .
See Problem 4.
Surveying The distance from you to the base of a tower on top of a hill is 2760 ft. The angle of elevation of the base is 26°.26 degrees . The angle of elevation of the top of the tower is 32°.32 degrees . Draw a diagram. Find to the nearest foot the height of the tower above the top of the hill.