The Sun hits a 30 foot flagpole at a 60° angle and casts an unobstructed 52 foot shadow. If a building is built 32 feet away, what height will the shadow strike the side of the building? (round to nearest tenth)

11.5 The angle does not really matter. Using similar triangles,

h/20 = 30/52

11.5 Lynn is correct

To solve this problem, we can use similar triangles. Let's call the height of the flagpole "x" and the height at which the shadow strikes the building "y".

We can set up a proportion using the corresponding sides of the two similar triangles formed by the flagpole, its shadow, and the building:

x/30 = y/32

Now, we need to find the value of "y".

First, let's find the value of "x" using the given information. We know that the Sun hits the flagpole at a 60° angle, so it forms a right triangle with the ground and the shadow. The opposite side of a 60° angle in a right triangle is equal to half the hypotenuse.

In this case, the opposite side is the height of the flagpole, which is "x", and the hypotenuse is 30 feet. Therefore, we have:

x = (1/2) * 30
x = 15 feet

Now, we substitute this value of "x" into our original proportion:

15/30 = y/32

To solve for "y", we can cross-multiply:

15 * 32 = 30 * y
480 = 30y

Dividing both sides by 30, we get:

y = 480/30
y = 16

So, the height at which the shadow strikes the side of the building is 16 feet.

The Sun hits a 30 foot flagpole at a 60° angle and casts an unobstructed 52 foot shadow. If a building is built 32 feet away, what height will the shadow strike the side of the building? (round to nearest tenth)

11.5

The angle does not really matter. Using similar triangles,

11.5

Lynn is correct

To solve this problem, we can use similar triangles. Let's call the height of the flagpole "x" and the height at which the shadow strikes the building "y".

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