1. Identify the known values: The horizontal distance from the observer to the tower is 87 feet. The angle of elevation to the top of the tower is 40°, and the angle of elevation to a point lower on the tower is 25°.
2. Let h1 be the height from the ground to the lower point (where the 25° angle points) and h2 be the height from the ground to the top of the tower (where the 40° angle points). The unknown length x is the vertical distance between these two points, so x = h2 - h1.
3. Use the tangent function for right triangles. For the smaller triangle (25° angle): tan(25°) = h1 / 87. Therefore, h1 = 87 * tan(25°).
4. For the larger triangle (40° angle): tan(40°) = h2 / 87. Therefore, h2 = 87 * tan(40°).
5. Calculate h1: h1 = 87 * tan(25°) ≈ 87 * 0.4663 ≈ 40.57 feet.
6. Calculate h2: h2 = 87 * tan(40°) ≈ 87 * 0.8391 ≈ 73.00 feet.
7. Calculate x: x = h2 - h1 ≈ 73.00 - 40.57 ≈ 32.43 feet.
8. Round the answer appropriately. The value of x is approximately 32.4 feet.
Parent Tip: Review the logic above to help your child master the concept of right triangle word problem worksheet.
