In triangle ABC, angle B is five times as large as angle A. The measure of angle C is 2° less than that of angle A. Find the measures of the angles. (Hint: The sum of the angle measures is 180°.)

Given ${\displaystyle b=2,a=3}$, and ${\displaystyle B=40}$ (degrees), determine whether this information results in one triangle, two triangles, or no triangle at all. Solve any resulting triangles.

Determine whether or not F is a conservative vector field. If it is, find a function f such that F=del f. F(x,y)=e^xsinyi+ e^xsinyj

For a rope course and climbing wall, a guy wire R is attached 47 ft high on a vertical pole. Another guy wire S is attached 40 ft above the ground on the same pole. Find the angle α between the wires if they are attached to the ground 50 ft from the pole.

Use the Law of Cosines to solve the triangles. Round lengths to the nearest tenth and angle measures to the nearest degree.
${\displaystyle a=5,b=5,c=5}$
${\displaystyle a=66,b=25,c=45}$

If the hypotenuse of a 45°-45°-90° triangle has a length of ${\displaystyle \surd 2}$, how long are the legs?

In triangle ABC with sides a, b, and c the Law of Sines states that

A right triangle has a cathetus of 75m, which is opposite to the anfle of 40.