https://file.aiquickdraw.com/mathbot/file/1725553818914okamdd77.jpg

We are tasked with finding the length of **RT** in the given right triangle. 

From the image:
- **∠T = 59°**, 
- **RS = 5.9** units (opposite side of angle 59°),
- **S is the right angle**.

To find **RT**, we can use trigonometric ratios. Since **RS** is the opposite side and we are looking for the hypotenuse **RT**, we will use the sine function:

\[
\sin(59^\circ) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{RS}{RT}
\]

Substitute the values:

\[
\sin(59^\circ) = \frac{5.9}{RT}
\]

Now solve for **RT**:

\[
RT = \frac{5.9}{\sin(59^\circ)}
\]

Let me calculate this.The length of **RT** is approximately **6.9** units.

Would you like more details on the solution or have any further questions?

Here are 5 related questions for practice:
1. How would you find the length of **TS** in this triangle?
2. What trigonometric ratio would you use if you were given the adjacent side instead of the opposite?
3. How do you find the angle **R** in the triangle?
4. What is the relationship between the sine and cosine of complementary angles in a right triangle?
5. How would the problem change if the angle given was an obtuse angle?

**Tip:** Always ensure that your calculator is set to degrees (not radians) when working with angles in degrees!

Find RT in the right triangle with ∠T = 59° and RS = 5.9 units. Write your answer as an integer or as a decimal rounded to the nearest tenth.

Learn how to find the hypotenuse RT in a right triangle where the angle T is 59° and the opposite side RS is 5.9 units. This trigonometry problem demonstrates the use of the sine function to calculate the length of the hypotenuse, suitable for students in Grades 9-10.

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