Answer:
i believe it is 2.0983
Step-by-step explanation:
I just tried to make a possible answer
Answer:
The lateral surface area of the triangular prism is 379.5sq units
Step-by-step explanation:
The side lengths of the base of the triangular prism are 5 meters, 8 meters, and 10 meters.
It is given that the height of the prism is 16.5 meters.
To determine the lateral surface area of the prism, let us use the formula
where a, b,c are the side lengths of the base of the triangular prism and h is the height of the prism.
Here and
Substituting these values in the formula, we have,
Simplifying, we get,
Multiplying, we get,
Thus, the lateral surface area of the triangular prism is
Answer:
The value of angle is 56.9°
Step-by-step explanation:
First, you have to find the length of hypotenuse using Pythagoras' Theorem, c² = a² + b² :
![{c}^{2} = {a}^{2} + {b}^{2}](https://tex.z-dn.net/?f=%20%7Bc%7D%5E%7B2%7D%20%20%3D%20%20%7Ba%7D%5E%7B2%7D%20%20%2B%20%20%7Bb%7D%5E%7B2%7D%20)
![let \: a = 8.25 \\ let \: b = 6.45](https://tex.z-dn.net/?f=let%20%5C%3A%20a%20%3D%208.25%20%5C%5C%20let%20%5C%3A%20b%20%3D%206.45)
![{c}^{2} = {8.25}^{2} + {6.45}^{2}](https://tex.z-dn.net/?f=%20%7Bc%7D%5E%7B2%7D%20%20%3D%20%20%7B8.25%7D%5E%7B2%7D%20%20%2B%20%20%7B6.45%7D%5E%7B2%7D%20)
![{c}^{2} = 68.0625 + 41.6025](https://tex.z-dn.net/?f=%20%7Bc%7D%5E%7B2%7D%20%20%3D%2068.0625%20%2B%2041.6025)
![{c}^{2} = 109.665](https://tex.z-dn.net/?f=%20%7Bc%7D%5E%7B2%7D%20%20%3D%20109.665)
![c = \sqrt{109.665}](https://tex.z-dn.net/?f=c%20%3D%20%20%5Csqrt%7B109.665%7D%20)
![c = 10.47cm \: (4s.f)](https://tex.z-dn.net/?f=c%20%3D%2010.47cm%20%5C%3A%20%284s.f%29)
In order to find θ, you have to apply Sine Rule :
![\sin(θ) = \frac{opposite}{adjacent}](https://tex.z-dn.net/?f=%20%5Csin%28%CE%B8%29%20%20%3D%20%20%5Cfrac%7Bopposite%7D%7Badjacent%7D%20)
![let \: oppo. = 8.77 \\ let \: hypo. = 10.47](https://tex.z-dn.net/?f=let%20%5C%3A%20oppo.%20%3D%208.77%20%5C%5C%20let%20%5C%3A%20hypo.%20%3D%2010.47)
![\sin(θ) = \frac{8.77}{10.47}](https://tex.z-dn.net/?f=%20%5Csin%28%CE%B8%29%20%20%3D%20%20%5Cfrac%7B8.77%7D%7B10.47%7D%20)
![θ = { \sin( \frac{8.77}{10.47} ) }^{ - 1}](https://tex.z-dn.net/?f=%CE%B8%20%3D%20%20%7B%20%5Csin%28%20%5Cfrac%7B8.77%7D%7B10.47%7D%20%29%20%7D%5E%7B%20-%201%7D%20)
![θ = 56.9 \: (1d.p)](https://tex.z-dn.net/?f=%CE%B8%20%3D%2056.9%20%5C%3A%20%281d.p%29)