1. **Problem Statement:** You have measurements for the reddish orange triangle and want to find the measurements for the white and blue triangles in a composite figure made of right triangles. 2. **Key Idea:** Use trigonometric relationships (sine, cosine, tangent) and the Pythagorean theorem to find unknown sides and angles in right triangles. 3. **Step 1: Identify Known Values for the Reddish Orange Triangle** - Hypotenuse $h_r = 11.3519$ (approx) - Angle opposite side $3.8$ cm is about $11.35^\circ$ 4. **Step 2: Use Sine and Cosine to Find Other Sides** - Opposite side $= h_r \times \sin(11.35^\circ) \approx 11.3519 \times 0.197 = 2.24$ cm - Adjacent side $= h_r \times \cos(11.35^\circ) \approx 11.3519 \times 0.981 = 11.14$ cm 5. **Step 3: Use These Sides to Find Corresponding Sides in White and Blue Triangles** - If white and blue triangles share sides or angles with the reddish orange triangle, use the known sides as references. - For example, if the white triangle shares the adjacent side with the reddish orange triangle, its side length is $11.14$ cm. 6. **Step 4: Apply Trigonometric Ratios in White and Blue Triangles** - Use known angles and sides to find missing sides: - $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$ - $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$ - $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$ 7. **Step 5: Use Pythagorean Theorem if Needed** - For right triangles, $a^2 + b^2 = c^2$ where $c$ is the hypotenuse. 8. **Summary:** Start with the reddish orange triangle's known hypotenuse and angles, calculate its sides using sine and cosine, then use these sides as references to find missing sides and angles in the white and blue triangles by applying trigonometric ratios and the Pythagorean theorem. This method allows you to systematically find all unknown measurements in the composite figure.