We are given that Miko and Tyler are visiting the Great Pyramid in Egypt. We know that they are standing 20 feet apart and that they are both 5.5 feet tall. Let y represent the horizontal distance from Tyler to the pyramid.
We are also given that their angles of elevation to the top of the pyramid are 48.6∘ and 50∘, respectively.
We are asked to evaluate how tall the pyramid is. To do this, notice that this height is the sum of the boys' height and the height of the pyramid above their line of sight. Let z represents the height above the boys line of sight.
To evaluate the lengths of the missing sides, we can use one of the trigonometric ratios. Let's recall that the tangent of ∠A is the ratio of the leg opposite ∠A to the leg adjacent ∠A. Using this definition, we can create the equations for tan50∘ and tan48.6∘.
⎩⎪⎨⎪⎧tan50∘=yztan48.6∘=20+yz(I)(II)
As we can see, we need to solve the system of equations. To do this, we can use the Substitution Method. Our first step will be to isolate z in the first equation.
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