Trigonometry Review Worksheet Answers

KEY Trig. Review Worksheet Name - _____________ Draw Diagrams. Show work. Round off all answers to one decimal place. (3 marks each) 1.) The angle of elevation of the Rock Mountain fire-control tower from the top of Blue Mountain 3.0 ݇݉ away (horizontal distance) is 18°. How much higher than Blue Mountain is the fire-control tower? ૙. ૢૠ ࢑࢓ 18° tan 18 = ௫ ଷ.଴ ‫ = ݔ‬0.9747 ‫ = ݔ‬0.97 ݇݉ 3.0 ݇݉ 2.) The angle of elevation of the summit from the bottom of the second lift at Snow Bowl is 33.0°. If a skier rides 1000. ݉ on this lift to the summit, what is the vertical distance between the bottom of the lift and the summit? ૞૝૞ ࢓ sin 33 = 33° ௫ ଵ଴଴଴. ‫ = ݔ‬544.639 ‫ = ݔ‬545 ݉ 1000 ݉ x 3.) The angle of depression of an aircraft carrier from an approaching airplane is 52.2°. If the plane is 700. ݉ above level of the deck of the carrier, how far away (horizontally) is the carrier? ૞૝૜ ࢓ x tan 52.2 = ଻଴଴ ௫. ‫ = ݔ‬542.9756 ‫ = ݔ‬543 ݉ 700 ݉ 52.2° 4.) The navigator on a bomber finds that the angle of depression of a target 4.00 ݇݉ away is 11.4°. At what altitude is the plane flying? ૙. ૡ૙ૠ ࢑࢓ 4.00 ݇݉ tan 11.4 = ௫ ସ.଴଴ ‫ = ݔ‬0.8065 ‫ = ݔ‬0.807 ݉ x 11.4° 5.) Billy's kite has a string 40. ݉ long and is flying 27 ݉ above his eye level. Find the angle of elevation of the kite. ૝૛° ߠ° sin ߠ = 40 ݉ ଶ଻ ସ଴. ߠ = 42.454 ‫ = ݔ‬42 ݉ 27 ݉ 1 KEY 6.) At an airport, cars drive down a ramp 96 ݉ long to reach the lower level baggage-claim area 13 ݉ below the main level. What angle does the ramp make with the ground at the lower level? ૠ. ૡ° sin ߠ = ଵଷ ߠ = 7.783 ଽ଺. ߠ = 7.8° ݉ 96 ݉ 13 ݉ ߠ° 7.) A surveyor standing in a ravine finds the angle of elevation of the top of one side is 15.13°. If he is standing 14 ݉ from the base of this side, how deep is the ravine? ૜. ૡ ࢓ 15.13° tan 15.13 = ௫ ଵସ. ‫ = ݔ‬3.785 ‫ = ݔ‬3.8 ݉ x 8.) As an airplane 14 ݉ m flying north passes directly over a civil defense air watch unit, another unit 4.30 ݇݉ due north finds the angle of elevation of the plane to be 19.17°. Find the altitude of the plane. ૚. ૞૙ ࢑࢓ tan 19.17 = x ௫ ସ.ଷ଴. ‫ = ݔ‬1.495 ‫ = ݔ‬1.50 ݇݉ 19.17° 4.30 ݇݉ 9.) Find the length of the altitude of an isosceles triangle whose base has length 20.0 ܿ݉ and whose base angles each has a measure of 45°. ૚૙. ࢉ࢓ tan 45 = ଵ଴.଴ ௫. ‫ = ݔ‬10 ‫ = ݔ‬10. ܿ݉ 45° 45° x 10.0 ܿ݉ 10.0 ܿ݉ 10.) A pendulum 40. ܿ݉ long is moved 30. ° from the vertical. How much is the lower end of the pendulum lifted? ૞. ૝ ࢉ࢓ 30° cos 30 = ௫ ସ଴. ‫ = ݕ‬40.0 − 34.64 40. ݉ ‫ = ݔ‬34.64 ‫ = ݕ‬5.35 ‫ = ݕ‬5.4 ݉ x 40. ݉ y 2 KEY 11.) The top of a vertical tree broken by the wind hits the ground 25.0 ݉ from the foot of the tree. If the upper portion makes an angle of 30.0° with the horizontal ground, what was the original height of the tree? ૝૜. ૜ ࢓ y tan 30 = ௫ ‫ = ݔ‬14.4337 ଶହ.଴ x cos 30 = 25.0 ݉ ଶହ.଴ ‫ = ݕ‬28.8675 ௬ 30° ℎ݁݅݃ℎ‫ ݔ = ݐ‬+ ‫ݕ‬ ℎ݁݅݃ℎ‫ = ݐ‬43.3 ݉ 12.) The angle of elevation of the top of Billings building from the roof of the Wolcott Building (in the same vertical plane) is 33.10°. As well, from the roof of the Wolcott to the 15th floor of the Billings building is 21.50°. If the distance between the roof and the 15th floor is 101 ݉, how far apart are the buildings? ૜ૢ૛ ࢓ ܻ + 101 x 1.) tan 33.10 = ௬ାଵ଴ଵ 2.) tan 21.50 = ௬ 33.10° ௫ ௫ ‫=ݔ‬ ௬ାଵ଴ଵ ୲ୟ୬ ଷଷ.ଵ଴ ‫=ݔ‬ ௬ ୲ୟ୬ ଶଵ.ହ଴ Combine 1 and 2 y ௬ାଵ଴ଵ x 21.50° ୲ୟ୬ ଷଷ.ଵ଴ = ௬ ୲ୟ୬ ଶଵ.ହ଴(௬ାଵ଴ଵ) ୲ୟ୬ ଶଵ.ହ଴ ୲ୟ୬ ଷଷ.ଵ଴ =‫ݕ‬ tan 21.50 (‫ ݕ‬+ 101) = (tan 33.10)‫ݕ‬ tan 21.50 ‫ ݕ‬+ tan 21.50 × 101 = (tan 33.10)‫ݕ‬ tan 21.50 × 101 = (tan 33.10)‫ ݕ‬− tan 21.50 ‫ݕ‬ 101.3939 = 0.25798‫ݕ‬ ‫ = ݕ‬154.216 ‫ = ݔ‬391.501 ‫ = ݔ‬392 ݉ 13.) From a point on the ground 75 ݉ from the base of a building, the angle of elevation of the top of a flagpole on the edge of the roof of the building is 45.20° and the angle of elevation of the bottom of the flagpole is 38.40°. Find the height of the pole. ૚૟ ࢓ ‫ݔ‬ 1.) tan 45.20 = 2.) tan 38.40 = 45.20° ௫ ଻ହ ௬ ଻ହ ‫ = ݔ‬75.525 ‫ = ݕ‬59.44 ‫ݕ‬ 38.40° ℎ݁݅݃ℎ‫ ݔ = ݐ‬− ‫ݕ‬ ℎ݁݅݃ℎ‫ = ݐ‬75.525 − 59.44 ℎ݁݅݃ℎ‫ = ݐ‬16.085 ℎ݁݅݃ℎ‫ = ݐ‬16.1 ݉ 75 ݉ 14.) How far from the vertical wall of a building is the base of a thirty-foot ladder, which makes a 75° angle with the ground? ૠ. ૡ ࢌ࢚ cos 75 = 75° ௫ ଷ଴. ‫ = ݔ‬7.7645 ‫ = ݔ‬7.8 ݂‫ݐ‬ 3 30 ݂‫ݐ‬ x