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1 Tim was standing at point A when he saw a tree, T, directly opposite him on the far bank of the river. He walked 100 m along the riverbank to point B and noticed that his line of sight to the tree made an angle of 27° with the riverbank. Answer the following to two decimal places. a How wide was the river? b What is the distance from point B to the tree? 27° A 100 m B Standing at B, Tim measured the angle of elevation to the top of the tree to be 18°. c Make a clearly labelled diagram showing distance TB, the height of the tree and the angle of elevation, then find the height of the tree. 2 A yacht, P, left port and sailed 45 km on a bearing of 290°. Another yacht, Q, left the same port but sailed for 54 km on a bearing of 040°. a What was the angle between their directions? b How far apart were they at that stage (to two decimal places)? 3 A biologist studying gum trees wanted to calculate the height of a particular tree. She placed a one metre ruler on the ground which cast a shadow on the ground measuring 1.5 m. The gum tree cast a shadow of 20 m, as shown in the diagram below (not to scale). Calculate the height of the tree. Give your answer to two decimal places. 20 m 1 m 1.5 m 4 A builder is digging a trench for a cylindrical water pipe. From a drain at ground level, the water pipe goes 1.5 m deep where it joins a storm water drain. The horizontal distance from the surface drain to the storm water drain is 15 m, as indicated in the diagram below (not to scale). 1.5 m Storm water drain 15 m Surface drain a Calculate the length of water pipe required to connect the surface drain to the storm water drain to two decimal places. b If the radius of the water pipe is 20 cm, what is the volume of the water pipe? Give your answer to two decimal places.

1 Tim was standing at point A when he saw a tree, T, directly opposite him on the far bank of the river. He walked 100 m along the riverbank to point B and noticed that his line of sight to the tree made an angle of 27° with the riverbank. Answer the following to two decimal places. a How wide was the river? b What is the distance from point B to the tree? 27° A 100 m B Standing at B, Tim measured the angle of elevation to the top of the tree to be 18°. c Make a clearly labelled diagram showing distance TB, the height of the tree and the angle of elevation, then find the height of the tree. 2 A yacht, P, left port and sailed 45 km on a bearing of 290°. Another yacht, Q, left the same port but sailed for 54 km on a bearing of 040°. a What was the angle between their directions? b How far apart were they at that stage (to two decimal places)? 3 A biologist studying gum trees wanted to calculate the height of a particular tree. She placed a one metre ruler on the ground which cast a shadow on the ground measuring 1.5 m. The gum tree cast a shadow of 20 m, as shown in the diagram below (not to scale). Calculate the height of the tree. Give your answer to two decimal places. 20 m 1 m 1.5 m 4 A builder is digging a trench for a cylindrical water pipe. From a drain at ground level, the water pipe goes 1.5 m deep where it joins a storm water drain. The horizontal distance from the surface drain to the storm water drain is 15 m, as indicated in the diagram below (not to scale). 1.5 m Storm water drain 15 m Surface drain a Calculate the length of water pipe required to connect the surface drain to the storm water drain to two decimal places. b If the radius of the water pipe is 20 cm, what is the volume of the water pipe? Give your answer to two decimal places.

Trigonometry (11th Edition)
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
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Complete solution please Answer should be 1. A. 50.95 m B. 112.23 m 3. 13.33 4. 1.89m^3
1 Tim was standing at point A when he saw a tree, T, directly opposite him on the far bank of the river. He walked 100 m along the riverbank to point B and noticed that his line of sight to the tree made an angle of 27° with the riverbank. Answer the following to two decimal places. a How wide was the river? b What is the distance from point B to the tree? 27° A 100 m B Standing at B, Tim measured the angle of elevation to the top of the tree to be 18°. c Make a clearly labelled diagram showing distance TB, the height of the tree and the angle of elevation, then find the height of the tree. 2 A yacht, P, left port and sailed 45 km on a bearing of 290°. Another yacht, Q, left the same port but sailed for 54 km on a bearing of 040°. a What was the angle between their directions? b How far apart were they at that stage (to two decimal places)?
Transcribed Image Text:1 Tim was standing at point A when he saw a tree, T, directly opposite him on the far bank of the river. He walked 100 m along the riverbank to point B and noticed that his line of sight to the tree made an angle of 27° with the riverbank. Answer the following to two decimal places. a How wide was the river? b What is the distance from point B to the tree? 27° A 100 m B Standing at B, Tim measured the angle of elevation to the top of the tree to be 18°. c Make a clearly labelled diagram showing distance TB, the height of the tree and the angle of elevation, then find the height of the tree. 2 A yacht, P, left port and sailed 45 km on a bearing of 290°. Another yacht, Q, left the same port but sailed for 54 km on a bearing of 040°. a What was the angle between their directions? b How far apart were they at that stage (to two decimal places)?
3 A biologist studying gum trees wanted to calculate the height of a particular tree. She placed a one metre ruler on the ground which cast a shadow on the ground measuring 1.5 m. The gum tree cast a shadow of 20 m, as shown in the diagram below (not to scale). Calculate the height of the tree. Give your answer to two decimal places. 20 m 1 m 1.5 m 4 A builder is digging a trench for a cylindrical water pipe. From a drain at ground level, the water pipe goes 1.5 m deep where it joins a storm water drain. The horizontal distance from the surface drain to the storm water drain is 15 m, as indicated in the diagram below (not to scale). 1.5 m Storm water drain 15 m Surface drain a Calculate the length of water pipe required to connect the surface drain to the storm water drain to two decimal places. b If the radius of the water pipe is 20 cm, what is the volume of the water pipe? Give your answer to two decimal places.
Transcribed Image Text:3 A biologist studying gum trees wanted to calculate the height of a particular tree. She placed a one metre ruler on the ground which cast a shadow on the ground measuring 1.5 m. The gum tree cast a shadow of 20 m, as shown in the diagram below (not to scale). Calculate the height of the tree. Give your answer to two decimal places. 20 m 1 m 1.5 m 4 A builder is digging a trench for a cylindrical water pipe. From a drain at ground level, the water pipe goes 1.5 m deep where it joins a storm water drain. The horizontal distance from the surface drain to the storm water drain is 15 m, as indicated in the diagram below (not to scale). 1.5 m Storm water drain 15 m Surface drain a Calculate the length of water pipe required to connect the surface drain to the storm water drain to two decimal places. b If the radius of the water pipe is 20 cm, what is the volume of the water pipe? Give your answer to two decimal places.
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