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hi bro plz solve fully accuratley these questions 

I'll begin by solving the problems from the images you've provided. Let’s go through the questions step by step.

### **Question 4: Aeroplane Distance**
The aeroplanes X and Y are at a height of 1500 m above the ground. You are given:
- Angle of elevation of plane X from point \(T = 58^\circ\)
- Angle of elevation of plane Y from point \(S = 77^\circ\)

We are to find the distance between the planes, which is \(RS\).

#### **Solution:**
The two triangles involved are right triangles with respect to the aeroplanes' heights. We can use the tangent function for each triangle.

For plane X:
\[
\tan(58^\circ) = \frac{1500}{RT} \quad \Rightarrow \quad RT = \frac{1500}{\tan(58^\circ)}
\]

For plane Y:
\[
\tan(77^\circ) = \frac{1500}{ST} \quad \Rightarrow \quad ST = \frac{1500}{\tan(77^\circ)}
\]

Since \(RS = ST - RT\), we will compute both distances.

Let me calculate the values now.It seems there is an issue, as the calculated distance \(RS\) between the two aeroplanes is negative, which isn't physically meaningful. This indicates that plane \(X\) might be closer to point \(T\) than plane \(Y\).

Let me recalculate with the correct approach, using absolute values for the horizontal distances between the points.It seems like I can't do more advanced data analysis right now. Please try again later.

Would you like me to help guide you through solving it manually instead?



Solve the trigonometry problems involving angles of elevation, distances between points, and unknown triangle side lengths.

Solve a set of trigonometry problems involving angles of elevation, distances between points, and unknown triangle side lengths. These problems use key concepts like sine, cosine, tangent, and the Pythagorean theorem. Suitable for students in Grades 10-12.

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