Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Relationships in Space: Geometry and Trigonometry in 2D and 3D, Exercise 12: Exercise 11C

The diagram shows a rectangular-based right-angled pyramid $ABCDT$ in which $AD=20 \mathrm{cm}, CD=15 \mathrm{cm}, TN=30 \mathrm{cm}$.

Find $TC$ . If the value is $k \mathrm{cm}$, then the value of $k$ is .....

The diagram shows a rectangular-based right-angled pyramid $ABCDT$ in which $AD=20 \mathrm{cm}, CD=15 \mathrm{cm}, TN=30 \mathrm{cm}$.

Find the angle between the edge.$\left[TC\right]$ and the base $ABCD.$

$M$ is the midpoint of $\left[DC\right]$.

The diagram shows a rectangular-based right-angled pyramid $ABCDT$ in which $AD=20 \mathrm{cm}, CD=15 \mathrm{cm}, TN=30 \mathrm{cm}$.

$M$ is the midpoint of $\left[DC\right]$.

Find the angle between the face $TCD$ and the base $ABCD, TMN.$

(Round off and write up to $1$ decimal place)

The Great Pyramid of Giza is a square-based pyramid. The base of the pyramid has side length $230.4 \mathrm{m}$ and the vertical height is $146.5 \mathrm{m}$. The Great Pyramid is represented in the diagram below as $ABCDE$. The vertex $E$ is directly above the centre $O$ of the base. $M$ is the midpoint of $BC$.

Calculate the volume of the pyramid. If the volume of the pyramid is $k {\mathrm{m}}^3$, then the value of $k$ is ..... (Round off and write up to $2$ decimal places)

The Great Pyramid of Giza is a square-based pyramid. The base of the pyramid has side length $230.4 \mathrm{m}$ and the vertical height is $146.5 \mathrm{m}$. The Great Pyramid is represented in the diagram below as $ABCDE$. The vertex $E$ is directly above the centre $O$ of the base. $M$ is the midpoint of $BC$.

Find $EM$. If the value of the $EM$ is $k \mathrm{m}$, then the value of $k$ is .....  (Round the answer to nearest integer)

The Great Pyramid of Giza is a square-based pyramid. The base of the pyramid has side length $230.4 \mathrm{m}$ and the vertical height is $146.5 \mathrm{m}$. The Great Pyramid is represented in the diagram below as $ABCDE$. The vertex $E$ is directly above the centre $O$ of the base. $M$ is the midpoint of $BC$.

Show that the angle between ​​​​​​$\left[EM\right]$ and the base of the pyramid is $52°$ correct to $2$ significant figures.

The Great Pyramid of Giza is a square-based pyramid. The base of the pyramid has side length $230.4 \mathrm{m}$ and the vertical height is $146.5 \mathrm{m}$. The Great Pyramid is represented in the diagram below as $ABCDE$. The vertex $E$ is directly above the centre $O$ of the base. $M$ is the midpoint of $BC$.

Find the total surface area of the pyramid including the base. If the total surface area of the pyramid is $k {\mathrm{m}}^2$, then the value of $k$ is ..... (Round off and write the answer to nearest integer, like if the answer is $293.7,$ then round it to $300$)

The Great Pyramid of Giza is a square-based pyramid. The base of the pyramid has side length $230.4 \mathrm{m}$ and the vertical height is $146.5 \mathrm{m}$. The Great Pyramid is represented in the diagram below as $ABCDE$. The vertex $E$ is directly above the centre $O$ of the base. $M$ is the midpoint of $BC$.

Find the angle between an edge and the base.  (Round off and write the answer in $1$ decimal place)