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3 years ago

3a+ 6 = 15, 3a = 9, a+ 2= 5, 1/3a =1

Mathematics

1 answer:

LekaFEV [45]3 years ago

7 0

Given parameters:

Find if any of the equations are the equivalent;

3a+ 6 = 15

3a = 9

a+ 2= 5

$\frac{1}{3a}$ =1

To find which of the equations are equivalent to one another, let us solve them first. The ones with the same solution are definitely equivalent.

(i) 3a+ 6 = 15

3a = 15 - 6

3a = 9

a = 3

(II) 3a = 9

a = 3

(III) a+ 2= 5

a = 5-2

a = 3

(IV) $\frac{1}{3a}$ =1

1 = 3a

a = $\frac{1}{3}$

We clearly see that the first three equations are equivalent.

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3 years ago

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3 years ago

If the angle of elevation of the sun is 61.7° when a building casts a shadow of 56.5 feet, what is the height of the building ro

maksim [4K]

SOLUTION

Let us use a simple diagram to interprete the question

In the diagram above, the dark stuff below represents the shadow and the rectangular bar represents the building. I have labelled the height of the building as h.

So we will use the right-angled triangle formed to find h

As we can see h represents the opposite side and 56.5 feet represents the adjacent side of the right-angle triangle. So we will use TOA

$\text{TOA tan }\theta=\frac{opposite}{\text{adjacent}}$

So we have

$\begin{gathered} \text{ tan }\theta=\frac{opposite}{\text{adjacent}} \\ \text{ tan }61.7\degree=\frac{h}{56.5} \\ 1.8572015=\frac{h}{56.5} \\ \text{cross multiplying, we have } \\ h=1.8572015\times56.5 \\ h=104.931887 \end{gathered}$

Hence the answer is 104.9 feet to the nearest tenth