Jack looks at a clock tower from a distance and determines that the angle of elevation of the top of the tower is 40°. John, who is standing 20 meters from Jack as shown in the diagram, determines that the angle of elevation to the top of the tower is 60°. If Jack’s and John’s eyes are 1.5 meters from the ground, how far is John from the base of the tower? Round your answer to the nearest tenth.
Ghulam sees the school 800m in the distance. He looks up to the top of the school and the angle of elevation is 32 degrees. Of Ghulam eyes are 1.5 meters above the ground, what is the height of the school, to the nearest metre ?
If the height of the tower is h higher than their eyes, and John is x away from the base,
h/x = tan 60°
h/(x+20) = tan 40°
Eliminating h, we get
x*tan60° = (x+20)*tan40°
Find x and add 1.5 to find the total height.
25.50meters
Thanks for the wrong answer
Thanks fot the wrong answer... really needed a negitave to my question...
To solve this problem, we can use the trigonometric concept of tangent.
Let's consider right triangle ABC, where A represents the top of the tower, B represents Jack's eyes, C represents John's eyes, and D represents the base of the tower.
We know that the angle of elevation from Jack is 40°, so we can label angle BAD as 40°.
Similarly, the angle of elevation from John is 60°, so we can label angle CAD as 60°.
Now, let's focus on triangle ABC. We can see that we are given the following measurements:
- BC: distance between Jack and John = 20 meters
- AB: height from Jack's eyes to the top of the tower = 1.5 meters
- AC: height from John's eyes to the top of the tower = ?
We need to find the value of AC, which represents the height from John's eyes to the top of the tower. To do this, we can use the tangent function.
Recall that the tangent of an angle is equal to the opposite side divided by the adjacent side.
In this case, in triangle ABC, the opposite side would be AB, and the adjacent side would be BC. So we can use the tangent function to write:
tan(40°) = AB / BC
Now, we can rearrange the equation to solve for AB:
AB = tan(40°) * BC
Using a calculator, we find:
AB ≈ tan(40°) * 20
Next, let's focus on triangle ACD. We need to find the value of AD, which represents the distance from John's eyes to the base of the tower.
We can use the tangent function again, this time for angle CAD:
tan(60°) = AC / BC
Now we can solve for AC:
AC = tan(60°) * BC
Using a calculator, we find:
AC ≈ tan(60°) * 20
Finally, to find the distance from John to the base of the tower, we can subtract AD from BC:
AD = BC - AC
Plugging in the values we found:
AD = 20 - (tan(60°) * 20)
Using a calculator, we find:
AD ≈ 20 - (1.732 * 20)
AD ≈ 20 - 34.64
AD ≈ -14.64
It seems like we made a mistake in our calculations, as we cannot have a negative distance. Let's try to find our error.