Trigonometry

Given a right spherical triangle whose given parts are \(a=82^\circ\) \(b=62^\circ\) and \(C=90^\circ\). What is the value of the side opposite the right angle?

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 A in the spherical triangle ABC, given \(a=106^\circ 25'\) \(c=42^\circ 16'\) and \(B=114^\circ 53'\)

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

Determine the spherical excess of the spherical triangle ABC given \(a=56^\circ\) \(b=65^\circ\) and \(c=78^\circ\)

What is the spherical excess of a spherical triangle whose angles are all right angles?

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

A spherical triangle has an area of 327.25 sq. km. What is the radius of the sphere if its spherical excess is 30°?

A ship on a certain day is at latitude \(20^\circ\) N and longitude \(140^\circ\) E. After sailing for 150 hours at a uniform speed along a great circle route, it reaches a point at latitude \(10^\circ S\) and longitude \(170^\circ\) E. If the radius of the earth is 3959 miles, find the speed in miles per hour.

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?

Given the triangle ABC in which A = 30°30′, b = 100 m and c = 200 m, find the length of side a.

Give the degree measure of the angle 3π/5 radians.

A motorboat moves in the direction N 40° E for 3 hours at 20 mph. How far north does it travel?

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.

5π/18 rad is how many degrees?

Simplify \(\dfrac{1}{\sec\theta - 1} + \dfrac{1}{\sec\theta + 1}\).

Find the base of an isosceles triangle whose vertical angle is 65 degrees and whose equal sides are 415 cm.

Simplify \(\dfrac{1}{\csc^2\theta}\).

Two angles measuring p degrees and q degrees are complementary. If \(3p - 2q = 40^\circ\), then the smaller angle measures

A ladder leans against the side of a building with its foot 12 ft from the building. How long is the ladder if it makes 70 degrees with the ground?