The length of a shadow of a building is 50 ft. Also, tan P = 0.8.
1.Write an equation involving a trigonometric ratio that can be used to find the height x of the building. Explain why your equation is correct.
2.Find the height x of the building by using your equation.
x/50 = 0.8
1. To find the height x of the building, we can use the trigonometric ratio of tangent. The tangent of an angle is defined as the ratio of the opposite side to the adjacent side of a right triangle. In this case, we can consider the angle P as the angle of elevation from the top of the building to the tip of its shadow.
Let's assume the height of the building is x and the distance between the building and the tip of its shadow is y. Therefore, the given information tells us that the length of the shadow is 50 ft.
According to the tangent ratio, tan P = opposite/adjacent = x/y. From the given information, we are also given that tan P = 0.8. Therefore, we can write the equation:
0.8 = x/y
This equation represents the relationship between the height of the building (x) and the distance between the building and the tip of its shadow (y).
2. To find the height x of the building, we need to determine the value of y, the distance between the building and the tip of its shadow. Since we are given the length of the shadow as 50 ft, we can substitute y = 50 into the equation:
0.8 = x/50
To solve for x, we can multiply both sides of the equation by 50:
0.8 * 50 = x
This simplifies to:
40 = x
Therefore, the height of the building is x = 40 ft.