Look at the picture

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

4 0

11 months ago

A segment with endpoint M Left parenthesis 5 comma 9 right parenthesis and N Left parenthesis 4 comma 3 right parenthesis is rot

mario62 [17]

Refer to the diagram below

If we draw a line that connects the center of rotation to one of the points, say point N, and take this line as the 0° position, then we need three 'turn' of 90° to get to 270°.

Coordinate of N' (-3, 4)
Coordinate of M' (-9, 5)