1 A city lot is in the shape of a triangle with sides 207 fe

1) A city lot is in the shape of a triangle with sides 207 feet, 198 feet, and 289 feet. Find each angle in the lot.

2) Points A and B are markers on opposite sides of a football field. If marker C is located on the field, 30 feet from marker B, and Angle C is 75 degrees and Angle A is 30 degrees, find the distance from points A to point B.

3) Find the angle of elevation of the sun if a 50.2 foot flagpole casts a shadow 73.2 feet long.

Solution

1) let a=207, ,b=198, c=289

COS A =(198 ²+289 ²-207² ) /2*198*289) = ( 39204+83521-424849 ) / 114444 =0.69

A= COS INVERSE(0.69)=46 degrees approx)

COSB =(207 ²+289 ²-198² ) /2*207*289)

B=43 DEGREES A[

C=91 DEGREES

2) a/SinA=b/ sin B =c/ sinC

30 /sin30 =x/sin 75

60 = x / 0.96

x=60 X0.96=57.6 is the distance

3)elevation of sun = inverse tan(theta)= inverse tan of (50.2/73.2)=46.4 degrees