University:
High School
Course:
High School Mathematics
Academic year:

2022
Views:

373

Pages:

3
Author:

Yasmine Burch

The Tangent Ratio In your own words, write the meaning of each vocabulary term. trigonometric ratio - ratio (fraction) of two sides of a right triangle 1 tangent - tan A = opposite leg / adjacent leg angle of elevation - the angle made with a horizontal line going "up" Core Concepts Tangent Ratio Let ΔABC be a right triangle with acute ∠A. The tangent of ∠A (written as tan A) is defined as follows. tan ∠A = length of leg opposite ∠A / length of leg adjacent to ∠A = BC / AC Since there are two "legs" on a right triangle, we need to make sure we are referencing the correct one. The Angle we are referencing is very important!!! So then tan B = AC / BC 9.4 Extra Practice In Exercises 1-3, find the tangents of the acute angles in the right triangle. Answer as a fraction and decimal. tan R = opp/adj = 45/24 = 15/8 tan B = opp/adj = 24/45 = 8/15 2. tan L = opp/adj = 7/5 tan K = opp/adj = 5/7 3. tan C = opp/adj = 2/√2 = √2 tan A = adj/opp = √2/2 In Exercises 4-6, find the value of x. 4. tan 10° = opp/adj = 5/x x(tan 10°) = 5 x = 5/tan 10° 5. tan 64° = opp/adj = x/13 13(tan 64°) = x 6. tan 31° = opp/adj = 24/x x(tan 31°) = 24 x = 24/tan 31° 7. In ΔCDE, ∠E = 90° and tan C = 4/3. Find tan D. tan D = 3/4 9.4 8. An environmentalist wants to measure the width of a river to monitor its erosion. a. From point A, she walks downstream 100 feet and measures the angle from this point to point C to be 40°. How wide is the river? Round to the nearest tenth. tan(40) = opp/adj = x/100 100 * tan(40) = x x ≈ 83.9 ft (width of the river) b. One year later, the environmentalist returns to measure the same river. From point A, she again walks downstream 100 feet and measures the angle from this point to point C to be now 51°. By how many feet has the width of the river increased? tan(51) = opp/adj = x/100 100 * tan(51) = x x ≈ 123.5 ft (new width of the river) The river is now 123.5 - 83.9 = 39.6 feet wider. 9. A boy flies a kite at an angle of elevation of 18°. The kite reaches its maximum height 300 feet away from the boy. What is the maximum height of the kite? Round to the nearest tenth. tan(18) = opp/adj = h/300 300 * tan(18) = h h ≈ 97.4 ft (maximum height of the kite)