3. Your neighbor puts tiger on his flat roof shed. You and another neighbor argue over the ht of the tiger. At a distance of 80 ft from the shed your angle of elevation from the ground level to the top of the shed is 5.74 degree. The angle of elevation to the top of the tiger from the same point is 13.37 degrees. To the nearest 10th foot how tall is the tiger
To find the height of the tiger, we can use trigonometry and set up a right triangle.
Let's say the height of the flat roof shed is represented by 'h' and the height of the tiger is represented by 't'. From the ground level, the line of sight to the top of the shed forms a right angle with the horizontal ground.
We can use the tangent function to find the height of the shed:
tan(5.74 degrees) = h / 80 ft
Now, let's consider the triangle formed by the line of sight to the top of the tiger:
tan(13.37 degrees) = (h + t) / 80 ft
We can rearrange both equations to solve for h and t separately:
h = 80 ft * tan(5.74 degrees)
h + t = 80 ft * tan(13.37 degrees)
Using a calculator, we can calculate the values:
h ≈ 80 ft * 0.1002 ≈ 8 ft
h + t ≈ 80 ft * 0.2398 ≈ 19 ft
Finally, to find the height of the tiger, we subtract the height of the shed from the total height:
t = (h + t) - h ≈ 19 ft - 8 ft ≈ 11 ft
Therefore, to the nearest 10th foot, the height of the tiger is approximately 11 feet.