Applications In Two And Three Dimensions
Muhtasari
How tall is a building you can see from 200 metres away? What angle does a diagonal make with the base of a box? These are everyday questions that trigonometry answers with precision. This topic takes the sine rule, cosine rule, and right-angled triangle ratios you already know and applies them to real situations in two and three dimensions.
You will learn to solve problems involving angles of elevation and depression, work with bearings, find lengths and angles inside 3D shapes such as cuboids and pyramids, and identify the angle between a line and a plane. Every technique builds on extracting the right triangle from a diagram, a skill that examiners reward heavily.
Malengo
- Solve problems in two or three dimensions using trigonometry
- Find angles between a line and a plane and between two planes
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- The angle of elevation from a point on the ground to the top of a 15 m tree is 35 degrees. What is the horizontal distance from the point to the base of the tree? A) 15 / tan 35 B) 15 tan 35 C) 15 sin 35 D) 15 / sin 35 Answer: A
- A cuboid has dimensions 3 cm by 4 cm by 12 cm. What is the length of the space diagonal? A) 12 cm B) 13 cm C) 15 cm D) 19 cm Answer: B
- Two sides of a triangle are 7 cm and 10 cm with an included angle of 60 degrees. What is the area? A) 35 sq cm B) 30.3 sq cm C) 17.5 sq cm D) 70 sq cm Answer: B
- The angle between a line and a plane is found using: A) The line and a normal to the plane B) The line and its projection onto the plane C) Two lines in the plane D) The line and the line of intersection Answer: B
- A ship sails 10 km north then 10 km east. The bearing of the ship from its starting point is: A) 045 B) 090 C) 135 D) 315 Answer: A
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Vitabu Vinavyopendekezwa
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Sehemu ya kitabu
Right Triangle Trigonometry
Use right triangles to evaluate trigonometric functions.
"Algebra and Trigonometry: Right Triangle Trigonometry" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/algebra-and-trigonometry/pages/7-2-right-triangle-trigonometry. Access for free at https://openstax.org/books/algebra-and-trigonometry/pages/1-introduction
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