Question

Find the shadow cast by a 10 foot lamp post when the angle of elevation of the sun is 58° .find the length to the nearest tenth of a foot.

Answer 1

Concept

Recall the  trigonometry formulas tan∅ = (opposite)/(Base).

Given

When the sun is at a 58° angle of elevation, a 10 foot light post casts a shadow.

To find

We have to find the length to the nearest tenth of a foot.

Solution

Let x be the length of the shadow cast.

We know tan∅ = (opposite)/(Base)

then

tan 58° = 10/x

x = 10/(tan 58°) foot

x = 6 . 24869 foot

Rounding to the nearest tenth of foot x = 6.2 foot

Hence length of the shadow cast is 6.2 foot.

Answer 2

Given data is

There is a 10-foot lamp, and the angle of elevation of the sun is

$58 \: degrees$

We need to find the length of the shadow.

Using trigonometry we can solve this problem easily.

For, that let's observe the diagram of the given data.

By observing the diagram, we have the opposite side of the angle and we need to find the adjacent side of the angle.

We can use the tan function to solve this problem as tan consists of the opposite side and the adjacent side.

Let us assume that the length of the shadow is

$x \:feet$

$\tan(x) = opposite \div adjacent \\ \tan(58) = 10 \div x \\ 1.6 = 10 \div x \\ x = 10 \div 1.6 \\ x = 6.25$

Therefore, the length of the shadow is 6.25 feet.

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