Trigonometric Ratios in Right Triangles

This video tutorial covers the basics of trigonometric ratios, including sine, cosine, and tangent, using right triangles. It explains how to calculate these ratios for given angles and sides, and introduces special right triangles like 30-60-90 and 45-45-90. The tutorial also demonstrates solving for missing sides and angles in right triangles using trigonometric principles, and provides example problems for practice.

In a right triangle, if the opposite side to angle A is 15 units and the hypotenuse is 17 units, what is the sine of angle A?

• 15/8

• 15/17

• 17/15

• 8/17

What is the cosine of angle A if the adjacent side to angle A is 8 units and the hypotenuse is 17 units?

• 17/8

• 8/17

• 15/17

• 8/15

For angle A in a right triangle, if the opposite side is 15 units and the adjacent side is 8 units, what is the tangent of angle A?

• 17/15

• 8/15

• 15/8

• 15/17

In a 30-60-90 triangle, what is the sine of 30 degrees?

• √2/2

• √3/2

• 1/2

• 1

What is the cosine of 60 degrees in a 30-60-90 triangle?

• 1

• √2/2

• √3/2

• 1/2

In a 45-45-90 triangle, what is the tangent of 45 degrees?

• √2/2

• 1/√3

• 1

• √3

If a right triangle has an angle of 40 degrees, an opposite side of x, and a hypotenuse of 12, what is the value of x?

• 9.7

• 8.7

• 7.7

• 10.7

Given a right triangle with an angle of 50 degrees, an adjacent side of 18, and a hypotenuse of y, what is the value of y?

• 18

• 24

• 28

• 32

If the opposite side to angle x in a right triangle is 300 units and the adjacent side is 200 units, what is the value of angle x?

• 45 degrees

• 60 degrees

• 56.3 degrees

• 30 degrees

In a right triangle, if cosine of angle A is 5/13 and the hypotenuse is 52 units, what is the sine of angle A?

• 5/13

• 48/52

• 12/13

• 20/52