The diagram shows a 9cm x 7cm rectangle-based pyramid. all the diagonal sides - TA, TB, TC, AND TD- are length 12cm. M is the midpoint of the rectangular base.
Work out angle TAC, to 1 decimal place.

[tex]\therefore cos (\angle TAM) = cos (\angle TAC) = \dfrac{\left (\dfrac{\sqrt{130} }{2} \right )}{12} = \dfrac{\sqrt{130} }{2 \times 12} = \dfrac{\sqrt{130} }{24}[/tex]

[tex]\angle TAC = arccos \left ( \dfrac{\sqrt{130} }{24} \right ) \approx 61.6 ^{\circ} \ to 1 \ decimal \ place[/tex]

MrRoyal MrRoyal · Answer 2 · 2021-12-04T11:24:04+01:00

The measure of angle TAC is 61.6 degrees

The given parameters are:

[tex]\mathbf{AB = 7}[/tex]

[tex]\mathbf{BC = 9}[/tex]

Start by calculating length AC, using the following Pythagoras theorem.

[tex]\mathbf{AC = \sqrt{AB^2 + BC^2}}[/tex]

So, we have:

[tex]\mathbf{AC = \sqrt{7^2 + 9^2}}[/tex]

[tex]\mathbf{AC = \sqrt{49 + 81}}[/tex]

[tex]\mathbf{AC = \sqrt{130}}[/tex]

[tex]\mathbf{AC = 11.40}[/tex]

Next, we calculate side length AM

[tex]\mathbf{AM = \frac{AC}{2}}[/tex]

So, we have:

[tex]\mathbf{AM = \frac{11.40}{2}}[/tex]

[tex]\mathbf{AM = 5.70}[/tex]

The measure of angle TAC is calculated using the following cosine ratio

[tex]\mathbf{cos(A)= \frac{AM}{TA}}[/tex]

So, we have:

[tex]\mathbf{cos(A)= \frac{5.70}{12}}[/tex]

[tex]\mathbf{cos(A)= 0.475}[/tex]

Take arc cos of both sides

[tex]\mathbf{A= 61.6}[/tex]

Hence, the measure of angle TAC is 61.6 degrees

The diagram shows a 9cm x 7cm rectangle-based pyramid. all the diagonal sides - TA, TB, TC, AND TD- are length 12cm. M is the midpoint of the rectangular base. Work out angle TAC, to 1 decimal place.

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The diagram shows a 9cm x 7cm rectangle-based pyramid. all the diagonal sides - TA, TB, TC, AND TD- are length 12cm. M is the midpoint of the rectangular base.
Work out angle TAC, to 1 decimal place.