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A steep mountain is inclined 74 degree to the horizontal and rises 3400 ft above the surrounding plain. A cable car is to be installed from a point 970 ft from the base to the top of the mountain. Find the shortest length of cable needed.

Respuesta :

lublana

Answer:

3917m

Step-by-step explanation:

We are given that

[tex]\theta=74^{\circ}[/tex]

[tex]h=3400 ft[/tex]

We have to find the shortest length of cable needed.

Let Base=x

We know that

[tex]tan\theta=\frac{Perpendicular\;side}{Base}[/tex]

Using the formula

[tex]tan74^{\circ}=\frac{3400}{x}[/tex]

[tex]x=\frac{3400}{tan74}=975m[/tex]

[tex]y=x+970=975+970=1945m[/tex]

Now, the length of cable needed

=[tex]\sqrt{(3400)^2+(1945)^2}[/tex]

=3917m

Hence, the shortest length of cable needed=3917m

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