Aboat is 400 feet away from one dock and 500 feet away from another dock.
the angle between the two paths is 45°. what is the approximate distance
between the docks?
o
a. 695 feet
o
o
o
b. 540 feet
c. 166 feet
d. 357 feet

The approximate distance  between the docks is 356.59 feet approximately.

Solution:

Given, A boat is 400 feet away from one dock and 500 feet away from another dock.  

The angle between the two paths is 45°.  

Now, Let d be the distance between the docks, which forms a third leg of a triangle for which the angle opposite it has measure 45 degrees.  

The other two legs have lengths 400 ft and 500 ft.

So, let us use the law of cosines:

where a, b, c are sides of triangle and C is angle opposite to side c.

Here in our problem, c = d, a = 400, b = 500 and C = 45

Hence, the distance between two docks is 356.59 feet approximately.

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.

the answer is: the length is 5/6 yards.

give me a or a 5 star rating if this is correct!

step-by-step explanation: