Without actually calculating the size of the angle you will be able to say that A B ^ C is obtuse using cos ( A B ^ C ) = - 11 24 , explain why you are able to do this.

Given, cos A B ^ C = - 11 24 Without calculating A B ^ C , we can say that A B ^ C is obtuse, because we know that cosine is negative in second and fourth quadrants. ⇒ A B ^ C ∈ 90 ° , 180 ° or 270 ° , 360 ° But an angle of triangle cannot be ≥ 180 ° Therefore A B ^ C ∈ 90 ° , 180 ° If an angle is > 90 ° , then the angle is called an obtuse angle. Hence, we can say that A B ^ C is an obtuse without calculating.

A square-based pyramid, with the coordinates of A ( 1 , 0 , 3 ) , B ( 1 , 5 , 3 ) and E ( 7 , 15 , 10 ) is shown. Find the midpoint of A B .

Given vertices are A ( 1 , 0 , 3 ) , B ( 1 , 5 , 3 ) and E ( 7 , 15 , 10 ) Midpoint of line joining points x 1 , y 1 , z 1 and x 2 , y 2 , z 2 is x 1 + x 2 2 , y 1 + y 2 2 , z 1 + z 2 2 . ∴ Midpoint of A B = 1 + 1 2 , 0 + 5 2 , 3 + 3 2 = 2 2 , 5 2 , 6 2 ∴ Midpoint of A B = ( 1 , 2 · 5 , 3 )

EASY

Diploma

IMPORTANT

Earn 100

A dockyard crane $A B C$ , is used to unload cargo from ships. $A B = 22.5 m, A C = 48 m$ and angle $A B C = 46 °$ . Find $A \hat{C} B$ .

Important Questions on Relationships in Space: Geometry and Trigonometry in 2D and 3D

MEDIUM

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 11 - Relationships in Space: Geometry and Trigonometry in 2D and 3D>Exercise 11I>Q 5

A dockyard crane $A B C$ , is used to unload cargo from ships. $A B = 22.5 m, A C = 48 m$ and angle $A B C = 46 °$ . Find the length of the lifting arm, $B C$ .

Question Image

MEDIUM

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 11 - Relationships in Space: Geometry and Trigonometry in 2D and 3D>Exercise 11I>Q 7

Two security cameras are positioned on the ceiling of a gym, $10 m$ apart. One camera has an angle of depression of $50 °$ to a point on the floor, and the other camera has an angle of depression of $60 °$ to the same point. Calculate the height, $h$ metres, of the gym.

Question Image

HARD

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 11 - Relationships in Space: Geometry and Trigonometry in 2D and 3D>Exercise 11I>Q 10

A ship leaves Shanghai on a bearing of

030 °

. It sails a distance of

500 km

to Jeju. At

B

, the ship changes direction to a bearing of

100 °

. It sails a distance of

320 km

to reach Nagasaki. Calculate the bearing and distance for the ship to return from Nagasaki to Shanghai.

EASY

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 11 - Relationships in Space: Geometry and Trigonometry in 2D and 3D>Exercise 11I>Q 12

Without actually calculating the size of the angle you will be able to say that

A \hat{B} C

is obtuse using

\cos (A \hat{B} C) = \frac{- 11}{24}

, explain why you are able to do this.

EASY

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 11 - Relationships in Space: Geometry and Trigonometry in 2D and 3D>Chapter review>Q 8

A square-based pyramid, with the coordinates of $A (1, 0, 3), B (1, 5, 3)$ and $E (7, \sqrt{15}, 10)$ is shown. Find the length $A B$ . [Enter the value excluding units]

Question Image

EASY

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 11 - Relationships in Space: Geometry and Trigonometry in 2D and 3D>Chapter review>Q 8

A square-based pyramid, with the coordinates of $A (1, 0, 3), B (1, 5, 3)$ and $E (7, \sqrt{15}, 10)$ is shown. Find the midpoint of $A B$ .

Question Image

EASY

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 11 - Relationships in Space: Geometry and Trigonometry in 2D and 3D>Chapter review>Q 8

A square-based pyramid, with the coordinates of $A (1, 0, 3), B (1, 5, 3)$ and $E (7, \sqrt{15}, 10)$ is shown. Find the length $A E$ . [Enter the value excluding units]

Question Image

EASY

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 11 - Relationships in Space: Geometry and Trigonometry in 2D and 3D>Chapter review>Q 12

Find the surface area of a tetrahedron with all faces equilateral triangles of side

6 cm

A dockyard crane ABC, is used to unload cargo from ships. AB=22.5m, AC=48m and angle ABC=46°. Find AC^B.

Important Questions on Relationships in Space: Geometry and Trigonometry in 2D and 3D

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A dockyard crane $A B C$ , is used to unload cargo from ships. $A B = 22.5 m, A C = 48 m$ and angle $A B C = 46 °$ . Find $A \hat{C} B$ .