https://file.aiquickdraw.com/mathbot/file/1726989273602r7r5otwc.jpg

Pemancar radio adalah teknologi yang digunakan untuk pengiriman sinyal dengan cara modulasi dan gelombang elektromagnetik. Gelombang ini bisa merambat melalui udara dan bisa juga merambat melalui ruang hampa udara.

Berikut disajikan gambar menara pemancar radio.
​
PT Radio Kita akan membangun menara pemancar radio baru dengan 4 kawat penyangga dipasang simetris pada menara tersebut, seperti tampak pada gambar berikut: Diketahui nilai tan 53° = 4/3. Jarak pemasangan ujung kawat pendek pada menara terhadap tanah (panjang CE) adalah ....

To solve for the distance \( CE \) (the height at which the shorter cable is attached to the tower), we can use trigonometry. From the image, we observe that triangle \( ACD \) (which includes angle 53°) and triangle \( ACB \) (with angle 60°) can be analyzed. The following details are available:

- The height of the tower, \( h = 22.52 \, \text{m} \).
- The horizontal distance between the base of the tower and the point where the shorter cable is anchored is \( CD = 15 \, \text{m} \).
- The angle \( \angle ACD = 53^\circ \).
- Given that \( \tan 53^\circ = 4/3 \), we can apply the tangent function to solve for \( CE \).

### Solution
We know the tangent of an angle is defined as:
\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]
For \( \triangle ACD \), using \( \angle ACD = 53^\circ \):
\[
\tan(53^\circ) = \frac{AE}{CD}
\]
Substituting \( \tan 53^\circ = 4/3 \) and \( CD = 15 \, \text{m} \), we get:
\[
\frac{AE}{15} = \frac{4}{3}
\]
Now, we can solve for \( AE \), and then calculate \( CE \) using the fact that \( AE + EC = AC \), where \( AC = 22.52 \, \text{m} \). Let me calculate the value.The length of \( AE \), the height from point \( E \) to the top of the tower, is \( 20 \, \text{m} \).

Now, to find the length of \( CE \), we subtract \( AE \) from the total height of the tower \( AC = 22.52 \, \text{m} \):
\[
CE = AC - AE = 22.52 - 20 = 2.52 \, \text{m}
\]

Thus, the distance \( CE \) (the height at which the shorter cable is attached) is \( 2.52 \, \text{m} \).

Do you have any further questions or would you like additional details? Here are some related questions for practice:

1. What is the length of the shorter cable based on the triangle formed by \( A \), \( C \), and \( D \)?
2. How would you calculate the length of the longer cable using the \( 60^\circ \) angle?
3. How would the solution change if the height of the tower was different?
4. How can we calculate the tension in the cables if the weight of the tower is provided?
5. What is the importance of the tangent function in solving problems involving right-angled triangles?

**Tip:** The tangent function is useful when we know an angle and one side of a right triangle and want to find the other side.

Pemancar radio adalah teknologi yang digunakan untuk pengiriman sinyal dengan cara modulasi dan gelombang elektromagnetik. Gelombang ini bisa merambat melalui udara dan bisa juga merambat melalui ruang hampa udara. PT Radio Kita akan membangun menara pemancar radio baru dengan 4 kawat penyangga dipasang simetris pada menara tersebut. Diketahui nilai tan 53° = 4/3. Jarak pemasangan ujung kawat pendek pada menara terhadap tanah (panjang CE) adalah ....

Learn how to calculate the height of the shorter cable attachment point on a radio transmission tower using the tangent function (tan 53° = 4/3). This trigonometry problem is ideal for students in Grades 9-12 and involves using the tangent formula to solve for CE in a right-angled triangle.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation