Trigonometry Answers

From a ship two lighthouses bear N 40o
E. After the ship has sailed 15 miles on a course of 135o
, they bear
10o
and 345o
, respectively. Find the distance between the two lighthouses.

Prove that, If 2 angles of a spherical triangle are equal, then the triangle is an isosceles spherical triangle.

1.) Isosceles triangle is similar to the Isosceles spherical triangle? justify your answer.
2.) An isosceles spherical triangle has an angle A=B= 54° and side b = 82°. Find the measure of the third angle.
3.) Determine the value of angle B of an isosceles spherical triangle ABC whose given parts are b=c= 54°28’ and a = 92°30’
4.) Solve for the side b of a right spherical triangle ABC whose parts of an isosceles spherical triangle are a = 46°, b = 75° and C = 90°.

Find the missing parts of an isosceles spherical triangle.
1.) a = b = 78°20’’ C = 118°50’
2.) A = B = 95°5’ C = 100°10’
3.) B = 72°48’ b = 64°52’
4.) A = C = 50°10’ c = 95°
5.) B = C = 78°44’ b = 18°16’

Solve the following quadrantal spherical triangle.
1.) a= 49° 23' , b = 76° 41'
2.) B = 100° , b = 50° 10'
3.) A = 121° 20' , B = 42° 01'
4.) a = 60° 35' , B = 122° 18'

Find the missing parts of an isosceles spherical triangle.
1.) 6. a = b = 78°20’’ C = 118°50’
2.) A = B = 95°5’ C = 100°10’
3.) B = 72°48’ b = 64°52’
4.) A = C = 50°10’ c = 95°
5.) B = C = 78°44’ b = 18°16’

Find the remaining parts of a quadrantal triangle (c = 90°). Write your answers on the space provided or use a separate sheet.
1.) a = 70°10’ b = 52°40’
2.) a = 116°53’ A = 122°39’
3.) b = 69°29.7’ B = 63°4.6’
4.) a = 106°38’ b = 36°49’
5.) A = 52°55’ b = 73°11’

The graph of a sinusoidal function has a minimum point at
(0, 2) and then has a maximum point at (3π,6). Write the formula of the function, where X is entered in radians.