Example 2 John wants to measure the length of the trunk of a tree. He walks exactly 35 m from the base of the tree, he lays down and looks up to the top of the tree. The angle from the ground to the top of the tree is 33 o. The tree grows at an angle of 83 o with respect to the ground. What is the length of the trunk of the tree to one decimal place?
Example 3 An architect designed a house and must give more instructions to the builders. The rafters that hold up the roof are equal in length. The rafters extend beyond the supporting wall by 5 inches. How long are the rafters? Express answer to the nearest inch
While golfing, Sarah hits a tee shot from T toward a hole H. Sarah hits the ball at an angle of 23 o to the hole and it lands at B. The score card says that H is 295 yards from T. Sarah walks 175 yards to her ball how far, to the nearest yard, is her ball from the hole?
Example 5 A 3 pointed star is made up of an equilateral triangle and 3 congruent isosceles triangles. Determine the length of each side of the equilateral triangle in this star to the nearest centimetre. 60 cm 20 o 60 cm Alternate strategy????
Example #6: Determine the perimeter of the regular decagon to the nearest tenth of a metre. 36 o
Homework While golfing, Beth hits a tee shot from point T toward a hole at H. However, the ball veers 34 and lands at B. The scorecard says that H is 250 m from T. Beth walks 120 m to her ball. Sketch a diagram of this situation. How far, to the nearest metre, is her ball from the hole? Show your work. ANSWER 165 m
Problems page 138 # 8 Page 129 #7 Page 125 #4, (#5 Page 172 #9
Homework page 1. A chandelier is suspended from a ceiling by 2 chains anchored at two different points on the ceiling. One chain is 46 cm long and forms a 60⁰ angle with the ceiling. The other chain is 64 cm long. What angle does the longer chain make with the ceiling? (Answer 38.5⁰) 2. Luke is flying his kite and released the entire 110m ball of string. He notices that the rope makes a 64⁰ angle with the ground (he is a math teacher s kid he notices stuff like that). His Mommy is on the other side of the kite and sees it at an angle of elevation of 30⁰. How far is Charlie from his Mommy? (Answer: 219.5m) 3. During a figure skating routine, Sally and Jon skate apart with an angle of 15⁰ between them. Sally skates for 5 meters and Jon skates for 7m. How far apart are the skaters? (answer: 2.5m) 4. Jill and Ryan are standing 15 m apart (facing each other), They both look up and spot a humming bird. The angle of elevations from Jill to the humming bird is 57 ⁰ and the angle of elevation from Ryan to the humming bird is 42⁰. How far is the humming bird from Jill to the nearest tenth of a metre? (Answer: 10.2 m) 5. A 4 m flag pole is not standing up straight. There is a wire attached to the top of the pole and anchored in the ground. The wire is 4.17m long. The wire makes a 68 angle with the ground. How far apart are the base of the flagpole and the wire anchored to the ground? (Answer:2.6 m OR 0.54 m) 6. friends are camping in the woods, Bert, Ernie and Elmo. They each have their own tent and the tents are set up in a Triangle. Bert and Ernie are 10m apart. The angle formed at Bert is 30. The angle formed at Elmo is 105. How far apart are Ernie and Elmo? (Answer:
Warm Up: Two helicopters are in the sky, when they are 5 km apart from each other they see a boat below them. If the angle of depression from the first helicopter to the boat is 42 o and the boat is 15 km from the first helicopter. How far away is the second helicopter from the boat? Round to one decimal place. Include a sketch #2 Homework Luke is flying his kite and release the entire 110 m ball of string. He notices that the rope makes. a 64 o angle with the ground. His Mommy is on the other side of the kite and sees it at an angle of elevation of 30 o. How far is Luke from his Mom?
Page 125 #4, #5 70 o The rafters that hold up the roof are equal in length. The rafters extend one foot beyond the supporting wall as shown. How long are the rafters? Express to nearest foot 36 feet one foot A. 36 feet B. 31 feet C. 32 feet D. 37 feet