3D Trigonometry Problems and Solutions
van Hiele Example
3D Trigonometry
Leaving Certificate Syllabus
What do students find difficult about 3D trigonometry?
How do you help students gain an understanding of 3D trigonometry?
… (The) study found a relationship
between young children’s construction
skills and strong number sense and
success in solving mathematical word
problems
(Nath & Szücs, 2014)
Children are as nonresponsive
to short term explicit instruction
on spatial transformation tasks
as adults.
(Ehrlich, Levine &
Goldin-Meadow, 2006)
3D Problems
A glass Roof Lantern in the shape of a pyramid has a rectangular base CDEF and its
apex is at B as shown. The vertical height of the pyramid is |AB|, where A is the point
of intersection of the diagonals of the base as shown in the diagram. Also |CD| = 2.5m
and |CF| = 3m
1.
Show that |AC|= 1.95m, correct to two decimal
places.
2.
The angle of elevation of B from C is 50° (i.e.
|
∠
BCA| = 50°). Show that |AB| = 2.3 m, correct to
one decimal place.
3.
Find |BC|, correct to the nearest metre.
A glass Roof Lantern in the shape of a pyramid has a rectangular base CDEF and its
apex is at B as shown. The vertical height of the pyramid is |AB|, where A is the point
of intersection of the diagonals of the base as shown in the diagram. Also |CD| = 2.5m
and |CF| = 3m
1.
Show that |AC|= 1.95m, correct to two decimal
places.
2.
The angle of elevation of B from C is 50° (i.e.
|
∠
BCA| = 50°). Show that |AB| = 2.3 m, correct to
one decimal place.
3.
Find |BC|, correct to the nearest metre.
Exploring the challenges students face with 3D trigonometry, ways to assist them in grasping concepts, and studies linking spatial skills to math problem-solving abilities. An example of a glass roof lantern pyramid problem is presented, involving calculations of distances and angles based on given dimensions.
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Presentation Transcript
van Hiele Example 3D Trigonometry
3D Problems What do students find difficult about 3D trigonometry? How do you help students gain an understanding of 3D trigonometry? (The) study found a relationship between young children s construction skills and strong number sense and success in solving mathematical word problems (Nath & Sz cs, 2014) Children are as nonresponsive to short term explicit instruction on spatial transformation tasks as adults. (Ehrlich, Levine & Goldin-Meadow, 2006)
1. Show that |AC|= 1.95m, correct to two decimal places. 2. The angle of elevation of B from C is 50 (i.e. | BCA| = 50 ). Show that |AB| = 2.3 m, correct to one decimal place. 3. Find |BC|, correct to the nearest metre. A glass Roof Lantern in the shape of a pyramid has a rectangular base CDEF and its apex is at B as shown. The vertical height of the pyramid is |AB|, where A is the point of intersection of the diagonals of the base as shown in the diagram. Also |CD| = 2.5m and |CF| = 3m
1. Show that |AC|= 1.95m, correct to two decimal places. 2. The angle of elevation of B from C is 50 (i.e. | BCA| = 50 ). Show that |AB| = 2.3 m, correct to one decimal place. 3. Find |BC|, correct to the nearest metre. A glass Roof Lantern in the shape of a pyramid has a rectangular base CDEF and its apex is at B as shown. The vertical height of the pyramid is |AB|, where A is the point of intersection of the diagonals of the base as shown in the diagram. Also |CD| = 2.5m and |CF| = 3m
