The line from Bob to the Peak of the mountain is the hypotenuse, and Bob's distance from the center base of the mountain is one leg, and the height of the mountain is the other leg. The 23o29' angle is between the hypotenuse and the leg from Bob to the Base (16194.6 ft). The side opposite to the angle is the height of the mountain.
The relevant trig function, then, is the tangent:
Tangent x = opposite side/adjacent side
Here the adjacent side is 16,194.6 feet and the opposite side is the height of the mountain. So
Tan(23.483o) = height/(16,194.6)
Solve for the height.
Answer:
The height of mountain= 197,185 foot.
Step-by-step explanation:
We are given that Bob is driving along a straight and level towards a mountain.
The measure of angle of elevation to the top pf the mountain =[tex]23^{\circ}29'[/tex]
The distance of Bob from the centre of the mountain base =16,194.6 feet.
We have to find the height of mountain.
Let height of the mountain=h feet
In a triangle ABC
AB=h feet
BC=16,194.6 feet
[tex] \angle C= 23^{\circ}29'[/tex]
[tex] 29'=\frac{29}{60}=0.48 [/tex]
[tex]\angle C=23+0.48=23.48^{\circ}[/tex]
[tex] 1^{\circ}=60'[/tex]
We know that [tex] tan\theta=\frac{perpendicular }{base}[/tex]
Substitute the values then we get
[tex] tan23.48^{\circ}=\frac{h}{16194.6}[/tex]
[tex] 12.176\times 16194.6=h[/tex]
[tex] h=197,185.4 foot[/tex]
h=197,185 foot
Hence, the height of mountain= 197,185 foot.
