Right Triangle Trigonometry Geometry 8.7 Applications of Right Triangle Trigonometry

Vocab Add hypotenuse, the three proportions, Pythagorean Theorem and Converse, multiply fractions vs. proportions, 45-45-90 and 30-60-90 formulas, pythagorean triples, sine, cosine, tangent, angle of elevation, angle of depression to vocab list

Solving Word Problems Use the 3 ratios – sin, cos and tan to solve application problems. Choose the easiest ratio(s) to use based on what information you are given in the problem.

Depression and Elevation If a person on the ground looks up to the top of a building, the angle formed between the line of sight and the horizontal is called the angle of elevation. If a person standing on the top of a building looks down at a car on the ground, the angle formed between the line of sight and the horizontal is called the angle of depression. horizontal angle of depression line of sight angle of elevation horizontal

From a point 80m from the base of a tower, the angle of elevation to the top of the tower is 28o. How tall is the tower?

1. From a point 80m from the base of a tower, the angle of elevation is 28˚. How tall is the tower? x 28˚ 80 Using the 28˚ angle as a reference, we know opposite and adjacent sides. Use tan tan 28˚ = 80 (tan 28˚) = x 80 (.5317) = x x ≈ 42.5 About 43 m

A ladder that is 20ft. is leaning against the side of a building A ladder that is 20ft. is leaning against the side of a building. If the angle formed between the ladder and the ground is 75o, how far is the bottom of the ladder from the base of the building?

2. A ladder that is 20 ft is leaning against the side of a building 2. A ladder that is 20 ft is leaning against the side of a building. If the angle formed between the ladder and ground is 75˚, how far is the bottom of the ladder from the base of the building? 20 building ladder 75˚ x Using the 75˚ angle as a reference, we know hypotenuse and adjacent side. Use cos cos 75˚ = 20 (cos 75˚) = x 20 (.2588) = x x ≈ 5.2 About 5 ft.

3. When the sun is 62o above the horizon, a building casts a shadow 18m long. How tall is the building?

3. When the sun is 62˚ above the horizon, a building casts a shadow 18m long. How tall is the building? x 62˚ 18 shadow Using the 62˚ angle as a reference, we know opposite and adjacent side. Use tan tan 62˚ = 18 (tan 62˚) = x 18 (1.8807) = x x ≈ 33.9 About 34 m

4. A kite is flying at an angle of elevation of about 55o 4. A kite is flying at an angle of elevation of about 55o. Ignoring the sag in the string, find the height of the kite if 85m of string has been let out.

4. A kite is flying at an angle of elevation of about 55˚ 4. A kite is flying at an angle of elevation of about 55˚. Ignoring the sag in the string, find the height of the kite if 85m of string have been let out. kite 85 x string 55˚ Using the 55˚ angle as a reference, we know hypotenuse and opposite side. Use sin sin 55˚ = 85 (sin 55˚) = x 85 (.8192) = x x ≈ 69.6 About 70 m

how far from the base of tower is the boulder? The angle of depression from the top of a tower to a boulder on the ground is 38o. If the tower is 25m high, how far from the base of tower is the boulder?

6. The angle of depression from the top of a tower to a boulder on the ground is 38º. If the tower is 25m high, how far from the base of the tower is the boulder? 38º angle of depression 25 Alternate Interior Angles are congruent 38º x Using the 38˚ angle as a reference, we know opposite and adjacent side. Use tan tan 38˚ = 25/x (.7813) = 25/x X = 25/.7813 x ≈ 32.0 About 32 m

Homework on binder paper. Answers: #5: 83m #7: 27m Finish Notes problems #5 and #7 on binder paper. Answers: #5: 83m #7: 27m Do pg. 318 #1-6 Vocab Test Tomorrow, Test Thursday