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1.
A meteorologist shines a spotlight vertically onto the
t shines a spotlight vertically onto the bottom of a cloud formation. He then places an angle-measuring
ters from the spotlight and measures a 74° angle of elevation from the ground to the spot of light on the
device 65 meters from the spotlight and me
clouds. How high are the clouds?

Respuesta :

The clouds are 226.68 meters above the spotlight.

Step-by-step explanation:

Step 1:

The angle measuring device is 65 meters from the spotlight and the angle of elevation from the ground to the spot of light is 74°.

So a right-angled triangle can be formed using these measurements. The angle of the triangle is 74° while the opposite side of the triangle measures x meters while the adjacent side of the triangle measures 65 meters.

We need to calculate the opposites side's length of the triangle.

Step 2:

Since we have the adjacent side's length and need to calculate the opposite side's length we use the tan of the given angle.

The opposite side of the triangle = x meters.

[tex]\tan \theta = \frac{oppositeside}{adjacentside} = \frac{x}{65}.[/tex]

[tex]tan 74 = 3.487, x = 3.487(65) = 226.07.[/tex]

So the spot of light is 226.07 meters above from the spotlight.

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