Fiona is repairing the wiring on a radio broadcast tower. She is in the basket of the repair truck 40m from the tower. if she looks up at an angle of 42° she can see the top of the tower. She can see the base if she looks down at an angle of 32°. How high is the tower?
it says the that the tower is 61 m high but i’m not sure how they get that
you can draw two right triangles
... her line of sight to the top and the bottom are along the hypotenuse
x = 40 tan(42º) ... y = 40 tan(32º)
...x + y = height of tower
John is repairing the wires on a radio broadcast tower that is 72 m high. He is in the basket of a repair truck. When he looks up, he estimates the angle of elevation to the top of the tower as 45 ̊. When he looks down, he estimates the angle of depression to the bottom of the tower as 35 ̊. What is the distance between the tower and the truck? Draw a
diagram.
To find the height of the tower, we can use trigonometry and the information given.
Let's assume that the height of the tower is represented by 'h'.
From the information given, we know that Fiona is 40m away from the tower and when she looks up at an angle of 42°, she can see the top of the tower. This forms a right triangle with the distance from the tower, height of the tower, and the line of sight from Fiona to the top of the tower.
Using trigonometry, we can determine the height of the tower based on the angle and the distance from the tower. The tangent of an angle is equal to the opposite side divided by the adjacent side.
So, we have:
tan(42°) = h/40
To find 'h', we can rearrange the equation:
h = tan(42°) * 40
Using a calculator, the tangent of 42° is approximately 0.9004. Now we can substitute this value into the equation:
h = 0.9004 * 40
h ≈ 36.02
Therefore, the height of the tower is approximately 36.02 meters.