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A school located due south of a park is 2.6 miles due east of a lake, as shown in the map. Which expression represents the distance between the school and the park?

2.6 ⋅ cos ⁡ ( 40 ∘ ) m i l e s

2.6 ⋅ tan ⁡ ( 40 ∘ ) m i l e s

2.6 /tan ( 40 ∘ ) m i l e s

2.6/cos (40 degree) miles

Will Give Brainliest A school located due south of a park is 26 miles due east of a lake as shown in the map Which expression represents the distance between th class=

Respuesta :

Answer:

The distance between the school and the park is [tex]2.6\times tan( 40) \ miles[/tex]

Step-by-step explanation:

Given the distance between lake and the school is [tex]2.6\ miles[/tex].

Also, the angle of inclination of park from lake is [tex]40[/tex]°.

We need to find the expression that represents distance between the park and the school.

We can see the given diagram is a right-angled triangle with adjacent [tex]2.6\ miles[/tex].

Taking

[tex]tan(40)=\frac{Opposite}{Adjacent}\\\\tan(40)=\frac{Opposite}{2.6}\\\\Opposite=2.6\times tan(40)[/tex]

So, the opposite of the triangle is  [tex]2.6\times tan( 40) \ miles[/tex]

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