a person standing 400 feet from the base of a mountain measures the angle of elevation from the ground to the top of the mountain to be 25 degrees, the person then walk 500 feet straight back and measures the angle of elevation to now be 20 degrees, how tall is the mountain?

draw the diagrams. Label the distance from the first position to the base of the peak as d, and the height of the Mountain from base as H.

H/d=tan25 or d=H/tan25

H/(d+500)=Tan20

solve for H.

829.27

Well, it seems like this mountain has a bit of a height complex! Let's help it out. We can use a little math to find its height.

First, let's break it down. The person initially measured the angle of elevation as 25 degrees when standing 400 feet away. After walking 500 feet straight back, they measured the angle as 20 degrees.

Now, let's take a step back and imagine a right triangle. The height of the mountain will be the vertical side, the base will be the distance between the person and the mountain, and the angle of elevation represents the angle formed between the ground and the line connecting the person's eye to the top of the mountain.

So, using some basic trigonometry, we can use the tangent function to find the height of the mountain.

We have the angle of 20 degrees, and the base of 900 feet (400 feet + 500 feet). The equation would look like this:

tan(20 degrees) = height / 900

Now, let's solve for the height:

height = tan(20 degrees) * 900

Calculating this, we find that the height of the mountain is approximately 326.52 feet. So, the mountain has finally reached new heights!

To find the height of the mountain, we can use trigonometry and create a right triangle.

Let's denote the height of the mountain as "h" (the side opposite the 25-degree angle), and the horizontal distance from the person's initial position to the base of the mountain as "x".

Now, we can use the tangent function. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side:

tan(25 degrees) = h / x

We know that x is 400 feet, so we can rewrite the equation as:

tan(25 degrees) = h / 400

Next, the person moves back 500 feet, so the new distance from the person's position to the base of the mountain is (400 + 500) = 900 feet. Let's denote this new distance as "y."

Using the same reasoning, we can find a new equation using the tangent of 20 degrees:

tan(20 degrees) = h / y

Substituting y = 900 into the equation gives us:

tan(20 degrees) = h / 900

Now, we have two equations:

tan(25 degrees) = h / 400 (Equation 1)
tan(20 degrees) = h / 900 (Equation 2)

To solve these equations simultaneously, we can use simple algebraic methods or a scientific calculator with trigonometric functions.

First, solve Equation 1 for h:

h = tan(25 degrees) * 400

Next, solve Equation 2 for h:

h = tan(20 degrees) * 900

Now that we have two values for h, we can equate them and solve for h:

tan(25 degrees) * 400 = tan(20 degrees) * 900

Rearranging and solving for h:

h = (tan(20 degrees) * 900) / tan(25 degrees)

Using a scientific calculator, we find that:

h ≈ 717.71 feet

Therefore, the height of the mountain is approximately 717.71 feet.

Tower 1 is 36° and it's 1675m away from tower 2, what is the elevation