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1 year ago

Instructions: Find the surface area of each figure. Round your answers to the nearest tenth, if necessary.

Mathematics

1 answer:

romanna [79]1 year ago

7 0

Answer:

surface area (rounded to the nearest tenth) : 282.7 yd²

Step-by-step explanation:

Formula ……………………………………………………………

surface area of a cylinder = 2 × (area of the base) + the lateral surface area

= 2πr² + 2πrh

= 2πr(r + h)

==================================

surface area of a cylinder = 2×π×3×(3+12)

= 282.743339 yd²

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In ∆ABC, m∠A = 60º, m∠C = 30º, and AB = 6 inches. What is the length of side BC?

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The length of the side BC is 6√3 inches

Step-by-step explanation:

Let us revise the sine rule

In Δ XYZ

The side XY is opposite to angle Z
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The sine rule is $\frac{XY}{sin(Z)}=\frac{YZ}{sin(X)}=\frac{XZ}{sin(Y)}$

In Δ ABC

∵ m∠A = 60°

∵ m∠C = 30°

∵ AB = 6 inches

- By using the sine rule

∵ AB is opposite to ∠C

∵ BC is opposite to ∠A

∵ $\frac{AB}{sin(C)}=\frac{BC}{sin(A)}$

∴ $\frac{6}{sin(30)}=\frac{BC}{sin(60)}$

- By using cross multiplication

∴ BC × sin(30) = 6 × sin(60)

∵ sin(30) = $\frac{1}{2}$ and sin(60) = $\frac{\sqrt{3}}{2}$

∴ $\frac{1}{2}$ BC = 6( $\frac{\sqrt{3}}{2}$ )

∴ $\frac{1}{2}$ BC = $3\sqrt{3}$

- Multiply both sides by 2

∴ BC = 6√3

The length of the side BC is 6√3 inches

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The tangent theta in a triangle is the ratio of sine theta and cos theta. It can be written as,

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Given information-

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The tangent theta in a triangle is the ratio of sine theta and cos theta. It can be written as,

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Simplify it further as,

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