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Artemon [7]
2 years ago
15

A small forest fire is cited due north of a fire lookout tower on Pikes Peak. From a second tower located 12.6 miles due west of

the first tower a Ranger observed that the fires is 49.5° east of duo North. How far is the fire from the tower Pikes Peak

Mathematics
1 answer:
Brums [2.3K]2 years ago
5 0

Answer:

10.76 miles

Step-by-step explanation:

<em>The following figure can be drawn from the information given.</em>

<em>We have to find the adjacent side which is between the given angle and 90 degrees.</em>

<em>Tan formula will be applied</em>

Tan (anlge) = opposite/adjacent

Opposite = 12.6

Angle = 49.5°

Adjacent = x

Tan (49.5°) = 12.6/x

x = 10.76 miles

Therefore, the fire is 10.76 miles away from the tower Pikes Peak.

!!

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Write expression as a sine or cosine of an angle.<br>cos 94° cos 18° + sin 94° sin 18° ​
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<h3>Answer:  cos(76)</h3>

=========================================================

Explanation:

The original expression is of the pattern cos cos + sin sin. This pattern matches the second identity in the hint. Specifically, we'll say the following:

cos(A - B) = cos(A)cos(B) + sin(A)sin(B)

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cos(94)cos(18) + sin(94)sin(18) = cos(94 - 18)

cos(94)cos(18) + sin(94)sin(18) = cos(76)

----------

We can verify this by use of a calculator. Make sure your calculator is in degree mode.

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