Identify a pari of similar figures and a pair of congruent figures. Explain your choices.
Are all rectangles similar? Justify your answer.
Are all squares similar? Justify your answer.
Evaluate the following, to four decimal places.
Solve for each angle, to the nearest degree.
\sin \theta = 0.8872
\triangle PQR. Express lengths to the nearest tenth of a centimetre and angles to the nearest degree.
AB = 19 m,
BC = 27 m
\angle B = 90°
a) Draw this triangle and label the given information.
\triangle ABC. Express lengths to the nearest metre and angles to the nearest degree.
Billy has lost track of time. He will get in trouble if he is late for dinner. but he will get in more trouble if he comes home with wet shoes. Racing home, Billy suddenly encounters a creek, as shown. Glancing at some nearby rocks. he estimates the distances indicated.
Billy can long jump about 2 m. Should he try to jump the creek, or take the long way home across the wooden bridge? Justify your reasoning.
Salma is at the top of a cliff looking down at Rico’s boat. They both have Global Positioning System (CPS) devices and are communicating via cell phones. They determine that Rico’s boat is 5.0 km from a point on the shore directly below Salma, and 6.0 km from Salma herself.
a) Draw a diagram to represent this situation and label the given information.
b) Find the angle of depression at which Salma is viewing Rico’s boat.
c) Find the height of the cliff.
From the top of the CN Tower, the angle of depression to the tip of the tower’s shadow is 88°. The shadow is 19.5 m long. How tall is the CN Tower?
Theresa and Branko are competing in a series of outdoor challenges that will eventually lead them to a hidden treasure. Each clue they find helps them find a new clue. Theresa is getting ready to climb a steep cliff to find their next clue at the Lookout Point. She has two options:
She is awaiting instructions from Branko, who is positioned directly facing Lookout Point at a distance of 30 m from the base of the cliff.
From Branko’s point of View, Lookout Point is at an angle of elevation of 68°. He also observes that the diagonal path up the cliff makes a 73° angle with the ground. Branko knows that Theresa can climb at a speed of 1.0 m/s and jog at a speed of 5.0 m/s after a climb. It is a tight race and seconds count. Which option should Branko tell Theresa to take: A or B?
A cat, sitting in the top of a tree, spots a dog and a firefighter, both on the flat ground below. From the cat’s point of view, the dog is 10 m south, at an angle of depression of 65°, and the firefighter is some distance east of the tree, at an angle of depression of 50°. How far is the firefighter from the dog?
A vertical communications tower is supported by two cables on opposite sides of the tower, as shown in the diagram. One cable is attached to the top of the tower and the other is attached to the tower at a height of 60 m. Both cables are attached to the ground with fasteners.
a) Verify that
\triangle ABC is similar to
\triangle EBD and list the corresponding sides and angles.
b) What is the height of the tower, to the nearest metre?
c) How long are the supporting cables, to the nearest metre?
d) How far apart are the cable fasteners, to the nearest metre?
Note: This is a simplified diagram. Normally it takes three or four cables to support a tower.