While visiting Wallawulla State Park, Joe approximated the angle of elevation to the top of a mound to be 40 degrees . After walking 450 feet closer, he guessed that the angle of elevation had increased by 18 degrees . Approximately how tall is the mound he was observing to the nearest foot?

Height of mound = 794 ft

Step-by-step explanation:

To illustrate the angle of elevation and distance, i have drawn it and attached below.

Now, from my diagram;

h = the height of the mound

At his first point of his trip to the foot of the mound, the angle of elevation is 40°, while the horizontal distance to the foot of the mound is "X"

So, by triangle definition,

tan(40°) = h/x

And so;

h = x tan40

h = 0.8391x  - - - - (eq 1)

At his second point of the trip to the foot of the mound, Joe is now,

"(x - 450) ft" from the foot of the mound.

Thus, his angle of elevation is 40 + 18 = 58°.

So, by triangle definition,

tan(58°) = h/(x - 450)

h = (x - 450)•(tan(58°))

h = 1.6003(x - 450)

h = 1.6003x - 720.135   - - - - -(eq2)

To get the height(h) of the mound, let's equate (eq1) to (eq2).

0.8391x = 1.6003x - 720.135

1.6003x - 0.8391x = 720.135

0.7612x = 720.135

x = 720.135/0.7612

x = 946.0523 ft

Let's put this value for x in eq (1);

h = 0.8391 x 946.0523 = 793.83 ft ≈ 794ft

(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

step-by-step explanation: