University:
Felician University
Course:
MATH-231 | Geometry I
Academic year:

2020
Views:

261

Pages:

4
Author:

StellarSymphony

**Trigonometry: Applications and Models** Solve the right triangle in the figure for all the unknown sides and angles. Round your answers to two decimal places. **1.** A = 30°, b = 3 B = 60° a = 1.73 c = 3.46 **2.** B = 71°, b = 24 A = 19° a = 8.21 c = 25.38 **3.** a = 3, c = 5 A = 36.87° B = 53.13° b = 4 **4.** a = 1.32, b = 4.71 A = 15.61° B = 74.39° c = 4.89 **5.** A = 43°18', c = 430.25 B = 46°42' a = 295.07 b = 313.12 **6. Find the length of a shadow cast by a building that is 100 feet tall if the angle of elevation of the sun is 25°.** 100 /| / | / | / | /____| x tan(25°) = 100/x x = 100 / tan(25°) x ≈ 214.45 ft **7. How tall is a park statue if the length of its shadow is 17.2 feet when the angle of depression of the sun is 53°?** x /| / | / | / | /____| 17.2 tan(53°) = x / 17.2 x = 17.2 * tan(53°) x ≈ 22.83 ft **8. What is the sun's angle of elevation if a 25-foot tall flagpole casts a shadow that is 9 feet long?** 25 /| / | / | /___| 9 tan(θ) = 25 / 9 θ = arctan(25/9) θ ≈ 70.20° **9. A 20-foot ladder leans against the side of a house. Find the height from the top of the ladder to the ground if the angle of elevation of the ladder is 80°.** 20 /| / | / | x / | /____| sin(80°) = x / 20 x = 20 * sin(80°) x ≈ 19.70 ft **10. From a point 50 feet in front of a church, the angles of elevation to the base of the steeple and the top of the steeple are 33.7° and 46.4°, respectively. Find the height of the steeple.** 46.4° /| / | / | / | x / | / | /______| 33.7° 50 tan(33.7°) = x / 50 x = 33.346 tan(46.4°) = (x + h) / 50 h = 50 * tan(46.4°) - 33.346 h ≈ 19.16 ft **11. An observer in a lighthouse 350 feet above sea level observes two ships directly offshore. The angles of depression to the ships are 4° and 6.5°. How far apart are the ships?** 350 /| / | / | / | /|_ x y-x tan(4.5°) = 350/x x = 4371.911 tan(6.5°) = 350/y y = 3071.911 y - x = 1300.00 ft **12. A passenger in an airplane sees two towns directly to the east. The angles of depression to the towns are 28° and 55°. If the towns are 12.3 kilometers apart, what is the elevation of the plane?** y /| / | / | / | /|_ x 12.3 - x tan(55°) = y / x tan(28°) = y / (x + 12.3) y * tan(55°) = y * tan(28°) + 12.3 * tan(28°) y(tan(55°) - tan(28°)) = 12.3 * tan(28°) y = 12.3 * tan(28°) / (tan(55°) - tan(28°)) y ≈ 7.296 km tan(55°) = x / y x = y * tan(55°) x ≈ 10.42 km **13. A cellular telephone tower that is 150 feet tall is placed on top of a mountain that is 400 feet above sea level. What is the angle of depression from the top of the tower to a cell phone user who is 5 horizontal miles away?** 150 /| / | / | / | /|_____________ 400 26400 ft tan(θ) = 950 / 26400 θ = arctan(950/26400) θ ≈ 2.06° **14. During take-off, an airplane's angle of ascent is 18° and its speed is 275 feet per second. (A) Find the plane's altitude after 1 minute. (B) At this rate, how long will it take the plane to climb to an altitude of 10,000 feet?** (A) x /| / | / | / | /____| 275 * 60 = 16500 ft sin(18°) = x / 16500 x = 16500 * sin(18°) x ≈ 5098.78 ft (B) sin(18°) = 10000 / x x = 10000 / sin(18°) x ≈ 32360.70 ft 32360.70 ft / 275 ft/sec ≈ 117.68 sec