The net of a pyramid is shown below:

Mathematics

1 answer:

Shalnov [3]3 years ago

6 0

Answer:

Step-by-step explanation:

height of pyramid = √(10²-(5/2)²) = √93.75

volume of pyramid = ⅓b²h = ⅓·5²√93.75 ≅ 80.69 in³

lateral area = 2×5×10 = 100 in²

base area = 5² = 25 in²

surface area = 100+25 = 125 in²

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A small plane and a large plane are 6.8km from each other, at the same altitude (height). From an observation tower, the two air

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Answer:

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Step-by-step explanation:

(a)See attached for the diagram representing this situation.

(b)

In Triangle ABC

$\text{Using Law of Sines}\\\dfrac{\sin A}{a}=\dfrac{\sin C}{c} \\\dfrac{\sin A}{5.2}=\dfrac{\sin 58^\circ}{6.8} \\\sin A=5.2 \times \dfrac{\sin 58^\circ}{6.8}\\A=\arcsin (5.2 \times \dfrac{\sin 58^\circ}{6.8})\\A=40.43^\circ$

Next, we determine the value of Angle B.

$\angle A+\angle B+\angle C=180^\circ\\40.43+58+\angle B=180^\circ\\\angle B=180^\circ-(40.43+58)\\\angle B=81.57^\circ$

Finally, we find b.

$\text{Using Law of SInes}\\\dfrac{b}{\sin B}=\dfrac{c}{\sin C} \\\dfrac{b}{\sin 81.57^\circ}=\dfrac{6.8}{\sin 58^\circ} \\b=\dfrac{6.8}{\sin 58^\circ} \times \sin 81.57^\circ\\b=7.9km $ (to the nearest tenth of a kilometer)$