How far up on a wall of a building will a 10-meter ladder reach if the foot of the ladder is 1,25 metres from the wall? Draw the situation and then explain your answer.

Question 1: Can a circular table top with diameter 2.7 metres long fit through a doorway 2.5 metres high and 1 metre wide? Why or why not? Step 1: Determine the maximum possible dimension an object can pass through the doorway. This maximum dimension is the length of the diagonal of the doorway. We use the Pythagorean theorem, where the height and width are the legs of a right-angled triangle, and the diagonal is the hypotenuse. Let h = 2.5 m (height) and w = 1 m (width). The diagonal d is given by: d = sqrt(h^2 + w^2) d = sqrt((2.5)^2 + (1)^2) d = sqrt(6.25 + 1) d = sqrt(7.25) d ≈ 2.6926 m Step 2: Compare the table's diameter with the doorway's dimensions. The table's diameter is 2.7 m. The doorway's height is 2.5 m. The doorway's width is 1 m. The doorway's diagonal is approximately 2.6926 m. Since the table's diameter (2.7 m) is greater than the doorway's height (2.5 m), width (1 m), and even its diagonal (2.6926 m), the table top will not fit. Yes/No: ❌ No Reason: The diameter of the table top (2.7 m) is greater than the maximum possible dimension it could pass through the doorway, which is the diagonal of the doorway (approximately 2.69 m). Question 2: How far up on a wall of a building will a 10-meter ladder reach if the foot of the ladder is 1.25 meters from the wall? Draw the situation and then explain your answer. This situation forms a right-angled triangle where: • The ladder is the hypotenuse (c = 10 m). • The distance from the wall is one leg (a = 1.25 m). • The height the ladder reaches up the wall is the other leg (b). Step 1: Apply the Pythagorean theorem. The Pythagorean theorem states a^2 + b^2 = c^2. (1.25)^2 + b^2 = (10)^2 Step 2: Calculate the squares. 1.5625 + b^2 = 100 Step 3: Solve for b^2. b^2 = 100 - 1.5625 b^2 = 98.4375 Step 4: Solve for b. b = sqrt(98.4375) b ≈ 9.9215 m The ladder will reach approximately 9.92 meters up the wall. Question 3: Find the length of the longest pole you could put in a rectangular storage room that is 12 units long, 9 units wide, and 8 units high? Explain. The longest pole that can fit in a rectangular room is the space diagonal of the room. This diagonal connects opposite corners of the room (e.g., from the bottom-front-left corner to the top-back-right corner). Step 1: Identify the dimensions of the room. Length (l) = 12 units Width (w) = 9 units Height (h) = 8 units Step 2: Apply the formula for the space diagonal (D). The formula for the space diagonal of a rectangular prism is: D = sqrt(l^2 + w^2 + h^2) D = sqrt((12)^2 + (9)^2 + (8)^2) Step 3: Calculate the squares of the dimensions. D = sqrt(144 + 81 + 64) Step 4: Sum the squared values. D = sqrt(289) Step 5: Calculate the square root. D = 17 units The length of the longest pole is 17 units. The last question about "the measures of the interior angles of the following..." is incomplete. Please provide the full question for me to solve it. What's next?