Find the height of triangle ABC

To find the height of triangle ABC, we first need to interpret the given information. We are given two side lengths, AC = 4 in and BC = 3.3. The diagram shows a height drawn from vertex C perpendicular to the base AB. For this problem to be solvable with only two side lengths and no angles or the base length, we must assume that triangle ABC is a right-angled triangle with the right angle at C. The height we need to find is the altitude to the hypotenuse. Step 1: Identify the given side lengths and assume a right angle. We have the lengths of the two legs of the right-angled triangle ABC: AC = 4 in BC = 3.3 in We assume C = 90^. Let h be the height from C to the hypotenuse AB. Step 2: Calculate the length of the hypotenuse AB. Using the Pythagorean theorem: AB^2 = AC^2 + BC^2 AB^2 = (4 in)^2 + (3.3 in)^2 AB^2 = 16 in^2 + 10.89 in^2 AB^2 = 26.89 in^2 AB = sqrt(26.89) in Step 3: Calculate the height h from C to AB. The area of a right-angled triangle can be expressed in two ways: Using the legs as base and height: Area = (1)/(2) × AC × BC Using the hypotenuse as base and h as height: Area = (1)/(2) × AB × h Equating these two expressions: (1)/(2) × AC × BC = (1)/(2) × AB × h h = (AC × BC)/(AB) Substitute the values: h = 4 in × 3.3 insqrt(26.89) in h = (13.2)/(sqrt(26.89)) in Step 4: Compute the numerical value. h ≈ (13.2)/(5.185556) in h ≈ 2.54558 in Rounding to two decimal places: h ≈ 2.55 in The height of triangle ABC is approximately 2.55 in. Send me the next one 📸