Exam 12: Introduction to Trigonometry

For right triangle ABC , m = 90 ° . If b = 8 and c = 12, find cos B (or cos ).

As increases in size from 0 ° to 90 ° , the value of cos also increases.

The sides of the square base of a regular pyramid measure 8 inches each while the altitude measures 10 inches. To the nearest degree, find the measure of the angle formed by the slant height and the apothem of square base of the pyramid shown.

In , b = 6.0 inches, m = 40 ° and m = 65 ° . To the nearest tenth of an inch, find the length c .

Using a calculator, the value of sin 54° is approximately 0.8090.

For the triangle with angle measures , , and for angles A , B , and C respectively, the area of the triangle can be calculated by using the formula .

The lengths of sides for a regular pentagon are 6 inches each. To the nearest tenth of an inch, find the length of the radius of the pentagon.

In the isosceles triangle shown, the legs are 10 inches each while m = 40 ° . Find the length of base correct to the nearest tenth of an inch.

In a right triangle with acute angle measures of and , sin . It follows that:

As increases from 0 ° to 90 ° , sin increases also.

In the figure, m = 90 ° and m = 29 ° . If c = 17.4, find b to the nearest tenth of unit..

In , is a right angle. If a = 5 and c = 13, find sin B (also known as sin )

In right triangle RST , m = 90 ° . If RS = 13 and ST = 17, find m to the nearest degree.

When = 90 ° , a form of the Law of Cosines reduces to Heron's Formula.

In the right triangle shown, it follows that tan 45° = 1.

The pitch (or slope)of a roof is . To the nearest degree, find the measure of the smaller acute angle shown in the drawing.

Find the exact value of cos 30°.

In , m = 42 ° while b = 5.6 and c = 7.2. To the nearest tenth of a square unit, find the area of the triangle shown.

Without using a calculator, which number is larger . . . cos 56° or cos 63°?

In a triangle, the angle measures are , , and and opposite sides have lengths a , b , and c respectively. Based upon the Law of Cosines, what expression is equivalent to ?