4.2.4 Application with Trigonometry

4.2.4 Application with Trigonometry

Multiple Choice

BELLWORK: Solve for the misssing distance

• 18.9 meters

• 19.5 meters

• 47.2 meters

• 27.5 meters

Multiple Choice

BELLWORK: Find the measure of the indicated angle.

• 9.39

• 55.2

• 20.2

• 19.4

Trigonometry Applications

Today we'll learn how to find missing distances and angles for word problems, using sine, cosine, and tangent (or their inverses).

How to solve:

1. Read the problem.

2. Draw a picture (right triangle).

3. Identify which part you need to find.

4. Use trig ratios or inverse trig ratios to solve.

Different Angles

Knowing which angle is the reference angle can be tricky.

ANGLE OF ELEVATION: "Looking" up.

ANGLE OF DEPRESSSION: "Looking" down.

Fill in the Blank

EXAMPLE 1: The Bungling Brothers Circus is in town and you are part of the crew that is setting up its enormous tent. The center pole that holds up the tent is 70 feet tall. To keep it upright, a support cable needs to be attached to the top of the pole so that the cable forms a 60 degree angle with the ground.

How long is the cable? Round to the nearest hundredth of a foot.

Fill in the Blank

EXAMPLE 2:

The circus decides to use a different cable that is attached to the ground, 50 feet from the center pole (that is still 70 feet tall). Now what is the angle of elevation, rounded to the nearest degree?

Multiple Choice

Elizabeth is flying a kite, which gets caught in the top of a tree. Use the diagram to estimate the height of the tree.

• 63.6 ft

• 1.59 ft

• 74.2 ft

• 86.9 ft

Multiple Choice

Jordan is stuck at the top of a Ferris wheel. Her mother is standing 38 feet from the base of the wheel watching her. If the angle of elevation from Jordan's mom to Jordan is 73^o, how far off the ground is Jordan?

• 118.2 ft

• 120.9 ft

• 124.3 ft

• 126.5 ft

Multiple Choice

Solve for the missing angle.

• 50.5 degrees

• 12.7 degrees

• 36.9 degrees

• 72.2 degrees

Multiple Choice

Which scenario describes the picture shown?

• A 5 foot ramp is 8 feet away from a building. What is the angle that the ramp makes with the ground?

• A 5 foot ramp leans against an 8 foot structure. What is the angle that the ramp makes with the ground?

• An 8 foot ramp leans

  against a building 5 feet away. What angle does the ramp make with the ground?

• A 5 foot man is 8 feet away from a building. What is the angle of elevation?

Multiple Choice

You are attacking an enemy castle. Your strategy is to go over the castle wall. You are 1500 meters away from the bottom of the wall. You measure the angle of elevation to the top of the wall at 3^o. How tall is the enemy castle wall?

• 78.6 meters

• 1498.0 meters

• 78.5 meters

• 75.3 meters

Multiple Choice

Kevin leans a 16 foot ladder l against a building. If the angle the ladder makes with the ground is 68°, how high up the building does the ladder reach?

• 39.6

• 6.0

• 14.8

• 13.6