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MATH 113: HOMEWORK 3, DUE FEBRUARY 10, 2009
(1) What is the connection between sine and right triangles?
(2) What is the connection between cosine and right triangles?
(3) What is the connection between tangent and right triangles?
(4) What is the connection between the Pythagorean theorem for right triangles and the identity sin^2 θ + cos^2 θ = 1?
(5) Draw a right triangle and label one of its acute angles as θ. Give labels to all three sides of the triangle. Now use this picture to deduce that sin θ = cos(π 2 − θ) whenever θ is an acute angle.
(6) Construct a right triangle such that one of it’s angles θ satisfies tan θ = 17/19.
(7) A 19 foot ladder is leaning against a wall. The base of the ladder is 6 feet from the wall. Find the height of the wall.
(8) A circle has radius 12 inches. A 40◦^ angle is drawn with its vertex at the center of the circle. What is the length of the chord AB connecting the points where the angle intercepts the circle?
(9) A cannon is located 2 miles away from the base of a tower. When the cannon is aimed at the top of the tower, its angle of elevation is 3◦. How tall is the tower?
(10) From a point A, Arthur Dent sees the top a pole at an angle of elevation of 60◦. Point B is located 25 metres away from point A, on the other side of the pole. From point B, Arthur sees the top of the pole at an angle of elevation of 42◦. How far is point A from the base of the pole?
(11) Marvin the paranoid android is walking towards a light tower. At some point he sees the top of the tower at an angle of elevation of 18◦, walking 20 metres further towards the tower he sees the top of the tower at an angle of elevation of 70◦. What is the height of the tower?
(12) From the top of a laser tower, Slartibartifast sees one end of a mine field at and angle of depression of 60◦. He then sees the other end of the mine field (in the same direction) at an angle of depression of 25◦. The mine field is 300 metres long. How high is the laser tower?
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(13) From the top of a building, Ford Prefect measures the angles of depression to the top and bottom of a 10-metre flag pole to be 40◦^ and 43◦, respectively. Find the height of the building.
(14) Dr Dan Streetmentioner is flying a kite on a windy day. The string is 180 feet long and the wind is strong enough to stretch it straight. Mrs Enid Kapelsen who is standing 140 feet from Dr Streetmentioner informs him that the kite is directly over her. How high above the ground is the kite?
(15) Mrs Alice Beeblebrox looks up at an angle of 28◦^ and sees the top of a tree and the top of a building algined. The tree is 20 metres away from Mrs Beeblebrox and the building is 60 metres away from her. What is the difference in heights between the building and the tree?
(16) Gag Halfrunt is walking north along the east bank of a river of molten lava. He sees a towel lying on the west bank of the river at an angle of 63◦^ from north. Walking 20 feet he sees the towel at 72◦^ from north. What is the width of the river?
(17) Two velociraptors, exactly 500 metres apart, observe a helicopter hovering directly above the line between them. One velociraptor estimates the angle of elevation to the helicopter as 46◦^ and the other estimates it as 32◦. What is the height of the helicopter?
(18) Two velociraptors are standing together under a tree. They start running (at the same speed) at an angle of 85◦^ to each other. After they have each run 30 metres, how far apart are they?
(19) You are sitting in a tree. You spot two velociraptors straight ahead, you estimate that the angles of depression to the velociraptors are 30◦^ and 45◦. You further esti- mate that the velociraptors are 20 feet apart. How high off the ground are you?
(20) In the construction of a house, the peak of the roof is supposed to make an angle of 140 degrees and rise 12 feet above the top of the walls. What is the furthest apart the walls can be for this to be possible?
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