Trigonometry and Triangle Properties

This video tutorial covers various methods to calculate missing side lengths of triangles. It begins with basic examples using the Pythagorean theorem and progresses to more complex problems involving trigonometry, including the use of SOHCAHTOA, and the laws of sines and cosines for non-right triangles. The tutorial also explores solving composite triangle problems using algebra and demonstrates the application of the geometric mean in triangle calculations.

What is the Pythagorean theorem used for in a right triangle?

• To calculate the perimeter

• To determine the type of triangle

• To find the missing side length

• To find the area of the triangle

In a right triangle, if the hypotenuse is 10 and one leg is 6, what is the length of the other leg?

• 8

• 7

• 5

• 9

Which trigonometric ratio would you use if you know the opposite side and the hypotenuse?

• Tangent

• Cosine

• Secant

• Sine

If the angle is 30 degrees and the hypotenuse is 50, what is the length of the opposite side using sine?

• 25

• 30

• 20

• 15

What is the Law of Sines used for?

• To calculate the perimeter of a triangle

• To find missing sides in non-right triangles

• To find the area of a triangle

• To determine the type of triangle

Given angle A is 50 degrees, angle B is 40 degrees, and side B is 10, what is side A using the Law of Sines?

• 11.9

• 9.8

• 10.5

• 12.3

When should you use the Law of Cosines?

• When you have two angles and a side

• When you have a right triangle

• When you have all three sides

• When you have two sides and the included angle

If two sides of a triangle are 9 and 10, and the included angle is 30 degrees, what is the length of the third side using the Law of Cosines?

• 7.03

• 6.02

• 5.01

• 8.04

What is the geometric mean of 8 and 32?

• 12

• 16

• 24

• 20

In a composite triangle, if the altitude to the hypotenuse is the geometric mean of the segments it divides, what is the altitude if the segments are 8 and 32?

• 14

• 16

• 20

• 18