Respuesta :
Answer:
Approximately 1.7 miles. high.
Step-by-step explanation:
Let h be the height of the mountain and x Β be the number of miles from the mountain when you take the first reading.
We have 2 right angled triangles Β One with adjacent side x and height h and another with adjacent side x-17 Β and height h so we have the system:
tan 3.5 = Β 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 = Β - 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.
The height of the mountain is 6.96 miles and this can be determined by using the trigonometric function.
Given :
- In traveling across flat land, you notice a mountain directly in front of you. Its angle of elevation (to the peak) is 3.5Β°.
- After you drive x = "17" miles closer to the mountain, the angle of elevation is 9Β°.
The trigonometric function can be used in order to determine the height of the mountain.
[tex]\rm tan \theta = \dfrac{P}{B}[/tex]
where P is the perpendicular and B is the base.
Now, substitute the values of the known terms in the avbove expression.
[tex]\rm tan 3.5 = \dfrac{H}{y}[/tex]
where y is the distance between mountain and vehical and H is the height of the mountain.
[tex]\rm y=\dfrac{H}{tan3.5}[/tex] Β Β --- (1)
Now, the trigonometric function when angle of welevation 9 degrees is given below:
[tex]\rm tan 9= \dfrac{H}{y-17}[/tex]
Simplify the above expression.
[tex]\rm y =17+\dfrac{H}{tan9}[/tex] Β --- (2)
Now, equate both the equations (1) and (2).
[tex]\rm \dfrac{H}{tan3.5}=\dfrac{H}{tan9}+17[/tex]
Simplify the above expression in order to determine the value of H.
H = 6.96 miles
For more information, refer to the link given below:
https://brainly.com/question/13710437
