Today, We Are Going to Begin the Study of Trigonometry, Which Means Triangle Measurement
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Geometry 300 Name______Trigonometry 1 Date______
Today, we are going to begin the study of trigonometry, which means triangle measurement.
Trigonometric ratios are ratios of the lengths of the sides of right triangles.
The three most common trigonometric ratios are sine (sin), cosine (cos), and tangent (tan)
Trigonometric ratios are related to the acute angles of a right triangle NOT the right angle.
If A and B are the acute angles of a right triangle, complete the following trig ratios…
Sin A = Sin B =
Cos A = Cos B =
Tan A = Tan B =
Example 1: Find sin M, cos M, tan M, sin N, cos N and tan N. Express each ratio as a fraction.
6 8
M 10 N
Example 2: Find the missing side lengths. Round to the nearest tenth.
a. b. Geometry 300 Name______Trigonometry 1 Date______Example 3: A 16-foot ladder is propped against a building. The angle it forms with the ground is 55˚. How far up the side of the building does the ladder reach?
We could also use trig ratios to solve for the acute angles of a right triangle. This involves using the inverse of the trig ratios.
Example 4: Find the approximate measure of ∠X. X
8 11
W Y
Example 5: Find the missing angle. Round to the nearest tenth.
a. b. Geometry 300 Name______Trigonometry 1 Date______
Homework:
Find the measure of x and y. Round side lengths and angles to the nearest tenth.
1. 2.
3. 4. Geometry 300 Name______Trigonometry 1 Date______
5. 6.
7. 8. Geometry 300 Name______Trigonometry 1 Date______
9. A ramp is to be built from a location 4 meters from the base of a loading dock. The dock is 1.2 meters up from the ground. What is the measure of the angle the ramp makes with the ground?
10. A guy wire is attached to a 100 foot tower that is perpendicular to the ground. The wire makes an angle of 55˚ with the ground. What is the length of the wire?