To measure the height of the Washington Monument, a student 5ft tall measures his shadow to be 4ft. At the same time of day, he measured the shadow of the Washington Monument to be 443ft long. Use a calculator to estimate the height of the monument to the nearest foot.
Question
To measure the height of the Washington Monument, a student 5ft tall measures his shadow to be 4ft. At the same time of day, he measured the shadow of the Washington Monument to be 443ft long. Use a calculator to estimate the height of the monument to the nearest foot.
Solution
Sure, let's solve this problem using the concept of similar triangles.
Step 1: Identify the ratios. The student's height to his shadow is 5ft/4ft = 1.25.
Step 2: Set up the proportion. If the student's height to shadow ratio is the same as the Washington Monument's height to shadow ratio, we can set up the following equation:
1.25 = h/443
where h is the height of the Washington Monument.
Step 3: Solve for h. Multiply both sides of the equation by 443 to solve for h:
h = 1.25 * 443 = 553.75
So, the height of the Washington Monument is approximately 554 feet when rounded to the nearest foot.
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