The angle of elevation of the top of a house from the bottom of a tower 160m high is 26 from the top of the tower the angle of elevation is 240degrees what is the height of the house if the tower and the house are 50m apart
I think the wording is very poor. It is a very TALL house if there is an angle of elevation from the top of the tower. First off,
The angle of elevation of the top of a house from the bottom of a tower is 26°, and the tower and the house are 50m does not need anything else. The height h is found using
h/50 = tan26°
The height of the tower does not even matter.
So, fix your question, and maybe show some work of your own, in case it is still unclear what you mean.
the angle of elevation of the top of a house from the bottom of a tower 160m high is a 26 From the top of the angle of elevation is 24 What is the height of the house if the tower and the house are 50m apart?
I think the angles of elevation is two
Tan24=h/50
h=50tan24
h=22.26
22.26+160=182.26
approximately 182.3m
To find the height of the house, we can use trigonometry. Let's break down the problem into two triangles: Triangle 1, which consists of the house, the tower, and the ground, and Triangle 2, which consists of the house, the tower, and the top of the tower.
First, we'll find the length of the base of Triangle 1, which is the horizontal distance between the house and the tower. We are given that the distance between the house and the tower is 50m.
Next, let's focus on Triangle 2. The angle of elevation from the top of the tower is given as 240 degrees. However, angles of elevation are typically measured as acute angles, which means we need to find the complementary angle first. The complementary angle of 240 degrees is 90 - 240 = -150 degrees. Since negative angles don't make sense in this context, we subtract -150 from 180 to get the acute angle: 180 - (-150) = 330 degrees.
Now we have the angle of elevation (330 degrees) and the length of the base (50m) for Triangle 2. We can use the tangent function to find the height of the tower.
tan(angle) = height/base
tan(330 degrees) = height/50m
To find the height, we rearrange the formula:
height = tan(330 degrees) * 50m
Now, let's calculate the height using a scientific calculator:
height = tan(330 degrees) * 50m ≈ (-1.732) * 50m ≈ -86.6m
Since the height cannot be negative in this context, we discard the negative sign and take the absolute value:
height = | -86.6m | = 86.6m
So, the height of the tower is approximately 86.6 meters.
Finally, to find the height of the house, we subtract the height of the tower (86.6m) from the total height observed at the bottom of the tower (160m):
height of the house = 160m - 86.6m = 73.4m
Therefore, the height of the house is approximately 73.4 meters.