In traveling across flat land, you notice a mountain directly in front of you. its angle of elevation (to the peak) is 3.5°. after you drive x = "17" miles closer to the mountain, the angle of elevation is 9°. approximate the height of the mountain. (round your answer to one decimal place.)

Approximately 1.7 miles. high.

Step-by-step explanation:

Let h be the height of the mountain and x  be the number of miles from the mountain when you take the first reading.

We have 2 right angled triangles   One with adjacent side x and height h and another with adjacent side x-17  and height h so we have the system:

tan 3.5 =  h / x

tan 9 = h / (x - 17)

h = x tan 3.5 and

h = (x - 17) tan 9 so

x tan 3.5 = (x - 17) tan 9

x tan 3.5 = x tan 9 - 17 tan 9

x =  - 17 tan 9 / ( tan 3.5 - tan 9)

= 27.69 miles

So h = x tan 3.5

= 27.69 * tan 3.5

= 1.7 miles approximate;y.

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