Answer:
tan 5π/24.
Step-by-step explanation:
We use the identity:
tan (A - B) = (tan A - tan B) / (1 + tan A tan B)
so the first expression simplifies to
tan ( π/3 - π/8)
= tan 5π/24.
<h3>The lateral area for the pyramid with the equilateral base is 144 square units</h3>
<em><u>Solution:</u></em>
The given pyramid has 3 lateral triangular side
The figure is attached below
Base of triangle = 12 unit
<em><u>Find the perpendicular</u></em>
By Pythagoras theorem
![hypotenuse^2 = opposite^2 + adjacent^2](https://tex.z-dn.net/?f=hypotenuse%5E2%20%3D%20opposite%5E2%20%2B%20adjacent%5E2)
Therefore,
![opposite^2 = 10^2 - 6^2\\\\opposite^2 = 100 - 36\\\\opposite^2 = 64\\\\opposite = 8](https://tex.z-dn.net/?f=opposite%5E2%20%3D%2010%5E2%20-%206%5E2%5C%5C%5C%5Copposite%5E2%20%3D%20100%20-%2036%5C%5C%5C%5Copposite%5E2%20%3D%2064%5C%5C%5C%5Copposite%20%3D%208)
<em><u>Find the lateral surface area of 1 triangle</u></em>
![\text{ Area of 1 lateral triangle } = \frac{1}{2} \times opposite \times base](https://tex.z-dn.net/?f=%5Ctext%7B%20Area%20of%201%20lateral%20triangle%20%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%20opposite%20%5Ctimes%20base)
![\text{ Area of 1 lateral triangle } = \frac{1}{2} \times 8 \times 12\\\\\text{ Area of 1 lateral triangle } = 48](https://tex.z-dn.net/?f=%5Ctext%7B%20Area%20of%201%20lateral%20triangle%20%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%208%20%5Ctimes%2012%5C%5C%5C%5C%5Ctext%7B%20Area%20of%201%20lateral%20triangle%20%7D%20%3D%2048)
<em><u>Thus, lateral surface area of 3 triangle is:</u></em>
3 x 48 = 144
Thus lateral area for the pyramid with the equilateral base is 144 square units
I think it depends on the area of the floor. You can figure that out if you
know the dimensions of the floor, like length and width and like that.
The best bench mark to use is an inch. She should use an inch because centimeters are too small and the steps might be less than a foot.