2. a surveyor measures the distance across a river that flows straight north by the following method. starting directly across from a tree on the opposite bank, the surveyor walks 100 m along the river to establish a baseline. she then sights across to the tree and reads that the angle from the baseline to the tree is 35°. how wide is the river?

The wide is 70.02 m.

Step-by-step explanation:

First you need to draw a triangle with only one 90 degrees angle.

The opposite side to the 90 degrees angle will be the hypotenuse.

We will call the remaining sides ''Baseline'' and ''River wide''.

The angle between hypotenuse and baseline is 35 degrees.

The triangle has one 90 degrees angle so we can apply the tangent equation

in the angles that are no 90 degrees.

Tangent (angle) = Opposite side/adjacent

Tan(35°)= River wide/100m

River wide = 100m.Tan(35°)

River wide = 70.02 m

step-by-step explanation:

(2x + 16) + (x) = 180

step-by-step explanation:

given,

abcd is a quadrilateral inscribed in a circle

angle a is labeled x plus 16, (x + 16)

angle b is labeled x degrees, (x)

angle c is labeled 6x minus 4, (6x – 4)

angle d is labeled 2x plus 16, (2x + 16)

what equation can be used to solve for angle b?

we know that the sum of the opposite angles of a simple quadrilateral inscribed in a circle is 180 degrees.

angle b is opposite angle d

therefore, angle b + angle d = 180

(x) + (2x + 16) = 180 

same as (2x + 16) + (x) = 180