Trigonometry

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?

If cot B = 5/2, find sin B.

A man 1.6 m tall casts a shadow 4 m long. Nearby, a flagpole casts a shadow 18 m long. How high is the flagpole?

Simplify \(\dfrac{1 + \tan^2 x}{1 - \tan^2 x}\).

An artist wishes to make a sign in the shape of an isosceles triangle with a 42 degree vertex angle and a base of 18 m. What is the area of the sign?

A 20-ft lamp post casts a 25 ft shadow. At the same time, a nearby building casts a 50 ft shadow. How tall is the building?

Simplify the expression \(\cos^2\theta - \sin^2\theta\).

\(\csc 520^\circ = ?\)

Simplify \(\dfrac{\cos A}{1 - \sin A} - \tan A\).

At a height of 23,240 ft, a pilot of an airplane measures the angle of depression of a light at an airport as 28°45′. How far is he from the light?

What is the angle of the sun above the horizon when a building 150 ft high casts a shadow of 405 ft?

Simplify \(\cos^2 x + \sin^2 x + \tan^2 x\).

Find the exact value of \(\dfrac{\tan 25^\circ + \tan 50^\circ}{1 - \tan 25^\circ\tan 50^\circ}\).

Two buildings with flat roofs are 60 m apart. From the roof of the shorter building, 40 m in height, the angle of elevation to the edge of the roof of the taller building is 40°. How high is the taller building?

Three ships are situated as follows: A is 225 mi due north of C, and B is 375 mi due east of C. What is the bearing of B from A?

A support wire is anchored 12 m up from the base of a flagpole and the wire makes a 15° angle with the ground. How long is the wire?

The base of an isosceles triangle is 20.4 and the base angles are 48°40′. Find the altitude of the triangle.