Standing on top of a slope of 5 degrees, i see the top of a building and an angle of elevation of 35degrees15'. i am 160cm tall and it is 12m from the building base. How tall is the building?

assuming you measure the 12m along the ground, we have

the horizontal distance from the base of the building is 12cos5° = 11.95

So, from eye level, the vertical distance to the top of the building is 11.95tan35°15' = 8.45

Add to that the 1.6m of your height, and subtract the rise in the ground of 12sin5° = 1.05m, and the building's height is

8.45+1.60-1.05 = 9.00 m

Thank you!

To find the height of the building, we can use trigonometry and the tangent function. Here's how you can do it:

1. Start by drawing a diagram to visualize the problem. Draw a triangle representing the situation. Label the angle of elevation as 35 degrees 15' and the slope as 5 degrees.

2. Since you're standing on a slope, you'll need to consider the effective height of your eyes. Subtract the height of your eyes (160 cm) from your actual height (the height from your eyes to the ground). Let's say your actual height is H. Therefore, the height from your eyes to the ground is H - 160 cm.

3. Calculate the length of the adjacent side of the triangle, which is the distance from the base of the building to your position. In this case, it is given as 12m.

4. Now, we can use the tangent function to find the height of the building. The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side. In this case, the opposite side is the height of the building (H_b) and the adjacent side is the distance from the base of the building to your position (12m). Therefore, the equation becomes:

tan(35 degrees 15') = (H_b - H + 160 cm) / 12 m

5. Solve the equation for H_b, the height of the building:

H_b = (tan(35 degrees 15') * 12 m) + H - 160 cm

Evaluate the tangent of 35 degrees 15' using a scientific calculator or a trigonometric table. The result will be in decimal form.

6. Finally, plug in the values you have and calculate the height of the building. Make sure to convert all units to the same system (e.g., meters or centimeters) for consistency.

H_b = (tan(35.25 degrees) * 12) + H - 160

Note: Remember to convert 160 cm to the same unit as H (meters or centimeters).

By following these steps, you should be able to find the height of the building.