Chapter 9 Triangle Trigonometry Section 9 1 Solving

Chapter 9: Triangle Trigonometry Section 9. 1: Solving Right Triangles

Right Triangle Recall: The parts of a right triangle: Hypotenuse Leg

Formulas for Right Triangle

Formulas for Right Triangle A way to remember these three formulas is the word SOHCAHTOA

Formulas for Right Triangle

Solving Right Triangles • In order to use all of the formulas, we need to remember one special theorem for right triangles. • Anyone remember that theorem and what it states?

Example 1: Given that the sin A = , find cosine and tangent of A.

Example 2: Given the diagram, find the value of angle B and the length of c.

Example 3: Given the diagram, find the value of angle A and angle B.

Example 4: Given the diagram below, find the value of a and b.

Example 5: Given the diagram below, find the value of a and c.

Solving Right Triangles • One thing I want you to remember is that for most of these problems, there are different ways to get the same answer. • Your work depends on the formulas that you decide to use based on the information that is given to you.

Angles of Elevation and Depression • Real-world problems that involve the solving of right triangles are those problems that deal with the angle of elevation and the angle of depression.

An angle of elevation is the angle formed by the horizon and an observer’s line of sight upward.

An angle of depression is the angle formed by the horizon and an observer’s line of sight downward.

Example 6: From a point 100 meters from the base of a tower, the angle of elevation to its top is 42 o. Find the height of the tower.

Example 7: From the top of a lighthouse 54 meters above the sea, the angle of depression of a buoy is 17 o. Find the horizontal distance from the buoy.

ASSIGNMENT pg. 334; 2 – 8 even, 13 – 15