DBA Student 3 * 4 0 Requ w Tools Help Student 3 Original Problem: Given the following scenario: Veronica enjoys a variety of leisure activities. Veronica has a reach of 26 inches, has a shoulder height of 5 feet, her eyes are 5 feet 6 inches from the ground. a. Veronica is hiking on a mountain. If the rock face makes a 62" angle with the ground, how far is her shoulder from the rock? Can she reach the rock without leaning or bending? b. Veronica is traveling and visits a city with a prominent statue. If she stands on a hill 120 feet from the statue and inclines her head 20 to look directly at the top of the statue, and the hill is at a 15" incline, how tall is the statue? C. A car on a straight road passes under a bridge. Standing on the bridge, 10 yards above the road, Veronica sees the car two and a half seconds later by declining her head 80. How fast is the car traveling, in miles per hour?okmarks CC 7 DBA Student 3 # 4 0 2 Request edit access iew Tools Help Student Work: a. Veronica is hiking on a mountain. If the rock face makes a 62 angle with the ground, how far is her shoulder from the rock? Can she reach the rock without leaning or bending? According to the diagram, the height of Veronica's shoulder is the "Opposite" side of the triangle. To find the distance her shoulder is from the rock, I need to find the "Adjacent" side of the triangle. This represents the Tangent function. Tan 0 = Opposite Adjacent Tan 62 = 5 Adjacent Tan 62 5 5(Adjacent) Adjacent - Tan 62 5 ~ 0. 376 feet The units are feet since the height of Veronica's shoulder is given in feet. Her arm length is given in inches, so it needs to be converted to inches to see if she can reach the rock. (0. 376) (12) - 4. 5 inchesdocs.google.com/document/d/1ZedsBN-MmkxCchoc bookmarks C Campus Parent Po.. |Classroom 26 calendar calculator Rapididentity G english 07 DBA Student 3 # 4 0 & Request edit access View Tools Help Yes, Veronica should be able to easily touch the rock since it's only 4.5 inches away and she can reach 26 inches. b. Veronica is traveling and visits a city with a prominent statue. If she stands on a hill 120 feet from the statue and inclines her head 20 to look directly at the top of the statue, and the hill is at a 15 incline, how tall is the statue? Similar to the problem from Part a, this problem uses tangent, for both the red and the blue triangles, except this time, the "Adjacent" measure is given and "Opposite" is needed. Blue Triangle Tan 0 - Opposite Adjacent Tan 20 Opposite 120 (120) (Tan 20) = (120) Opposite 120docs.google.com/document/d/126dsBN-MmkxCchSEWillAqkEeG_UoW9arkTGIWA pokmarks C Campus Parent Po.. _ Classroom 26 calendar calculator . Rapididentity G english 07 DBA Student 3 # 4 0 & Request edit access View Tools Help Opposite = (120) (Tan 20) Opposite ~ 43. 676 feet Red Triangle Tan 0 Opposite Adjacent Tan 15 = Opposite 120 (120) (Tan 15) = (120) (-Opposite 120 Opposite = (120) (Tan 15) Opposite ~ 32. 154 feet Height of the statue = Opposite side of the Blue Triangle + Opposite side of the Red Triangle Height of the Statue ~ 43. 676 + 32. 154 Height of the Statue = 75, 830 feet C. A car on a straight road passes under a bridge. Standing on the bridge. 10 yards above the road. Veronica sees the car two and a half seconds later by declining her head 89. How fast is the car traveling, inCALCULUS B - > Lesson 6.0/ DBA docs.google.com/document/d/126dsBN-MmkxCchSEWi1 IAqkEeG_UoW9arRtqlWx4zoo/edit bookmarks C Campus Parent Po.. _ Classroom 26 calendar calculator Rapididentity G english .07 DBA Student 3 # 4 0 & Request edit access View Tools Help C. A car on a straight road passes under a bridge. Standing on the bridge, 10 yards above the road, Veronica sees the car two and a half seconds later by declining her head 80. How fast is the car traveling, in miles per hour? Also a Tangent problem, this scenario compares the distance traveled with the height of the bridge. Distance traveled is "Adjacent" and height of the bridge is "Opposite". The Triangle Sum Theorem says that the Sum of the Angles in a Triangle is 180 degrees. 8 + x + 90 = 180 98 + x = 180 98 + X 98 = 180 - 98 180 - 98 82 Tan O - Adjacent Tan 82 =CALCULUS B - X Lesson 6.07 DBA Student A docs.google.com/document/d/126dsBN-MmkxCchSEWi1IAqkEeG_UoW9arRtqlWx4zoo/edit bookmarks C Campus Parent Po. = Classroom 26 calendar / calculator . Rapididentity G english .07 DBA Student 3 # 4 0 6 Request edit access View Tools Help 8 + x + 90 = 180 98 + x = 180 98 + x - 98 - 180 - 98 x = 180 - 98 X = 820 Opposite 22 Tan 0 Adjacent 10 Tan 82 = Adjacent Tan 82 10 23 10 10(Adjacent) Adjacent = 10 Tan 82 - 71. 154 yards The car travels this distance in two and a half seconds, so speed needs to be converted to miles per hour from yards per second. 1 yard = 3 feet mile = 5280 feet second SHA minutes hour miles 5260 60CALCULUS B - X Lesson 6.07 DBA Student 3 - Goc x docs.google.com/document/d/126dsBN-MmkxCchSEWi1 IAqkEeG_UoW9arRtqlWX4zoo/edit t bookmarks C Campus Parent Po. |Classroom 20 calendar calculator \\ Rapididentity G english 6.07 DBA Student 3 + 4 0 & Request edit access View Tools Help 1 yard = 3 teet 1 mile = 5280 feet yards (feet miles seconds minutes seconds yards feet minutes hour (miles 60 27 2.5 5280 60 hour 28 (71.154)(3) (1)(60) miles (2.5)(1)(5280)(60) hour 29 12807.6655 miles 792000 hour I 25 The car is traveling at 61.84 miles per hour