Trigonometry

Determine the value of the angle B of an isosceles spherical triangle ABC whose given parts are \(b=c=54^\circ 28'\) and \(a=92^\circ 30'\)

Solve for angle C of the oblique triangle ABC given, \(a=80^\circ\) \(c=115^\circ\) and \(A=72^\circ\).

The area of spherical triangle ABC whose parts are \(A=93^\circ 40'\), \(B=64^\circ 12'\), \(C=116^\circ 51'\) and the radius of the sphere is 100 m is

An observer wishes to determine the height of a tower. He takes sights at the top of the tower from A and B, which are 50 ft apart, at the same elevation on a direct line with the tower. The vertical angle at point A is 30 degrees and at point B is 40 degrees. What is the height of the tower?

Two stones are 1 mile apart and are at the same level as the foot of a hill. The angles of depression of the two stones viewed from the top of the hill are 5 degrees and 15 degrees respectively. Find the height of the hill.

A wall is 15 ft high and 10 ft from a house. Find the length of the ladder which will just touch the top of the wall and reach a window 20.5 ft above the ground.

A train is moving at the rate of 8 mi/h along a piece of circular track of radius 2,500 ft. Through what angle does it turn in 1 min?

Three circles of radii 3, 4 and 5 inches, respectively, are tangent to each other externally. Find the largest angle of the triangle found by joining the centers of the circles.

If the tangent of angle A is equal to the square root of 3, with angle A in the 3rd quadrant, find the square of the tangent of A/2.

A tower 150 m high is situated at the top of a hill. At a point 650 m down the hill, the angle between the surface of the hill and the line of sight to the top of the tower is 12°30′. Find the inclination of the hill to a horizontal plane.

What is the value of x in \(\arctan 3x + \arctan 2x = 45^\circ\)?

From a hill 600 ft high, the angles of depression to the bases in opposite directions are 42° and 19°23′ respectively. Find the length of the proposed tunnel through the bases.

Points A and B are 100 m apart and are of the same elevation as the foot of a building. The angles of elevation of the top of the building from points A and B are 21 degrees and 32 degrees respectively. How far is A from the building?