From the top of a building 120m high, the angle of depression of two cars on the ground in line with the base of the building are 18' and 65' respectively. Calculate the distance between the cars.
To solve this problem, we can use trigonometry and the concept of angle of depression.
Step 1: Draw a diagram
Start by drawing a diagram to visualize the situation. Label the height of the building as 120m and the angles of depression as 18' and 65'. We want to find the distance between the two cars.
Step 2: Use trigonometry
Since we are dealing with right triangles, we can use trigonometric functions such as tangent (tan) to find the information we need.
Let's consider the first car.
In the right triangle formed by the car, the top of the building, and the ground, the angle of depression is 18'. The opposite side to this angle is the height of the building (120m), and we want to find the adjacent side, which represents the horizontal distance to the first car.
Using the tangent function:
tan(angle) = opposite / adjacent
tan(18') = 120 / adjacent (let's call it x)
Solving for x:
x = 120 / tan(18')
Repeat the same process for the second car, using the angle of depression of 65'.
Step 3: Calculate the distances
Using the values calculated in step 2, find the distances to each car.
First car:
x1 = 120 / tan(18')
Second car:
x2 = 120 / tan(65')
Step 4: Calculate the distance between the cars
To find the distance between the two cars, we subtract the distances calculated in step 3.
Distance = x2 - x1
Substitute the values and calculate the distance to get the final answer.
Do you really mean 18 minutes and 65 minutes or do you mean degrees?
A1 = 90 - 18 whatever
A2 = 90 - 65 whatever
d1 = 120 tan A1
d2 = 120 tan A2
what is d1 - d2 ?