on a sunny day a 36 inch yard stick casts a 21 inch shadow how tall is the building whose shadow is 168 feet

288 feet

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3 x 168 /1.75 = 288

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To find out the height of the building, we can use the concept of similar triangles. Let's break down the problem and solve it step by step:

Step 1: Determine the scale factor
The yardstick's shadow and the building's shadow are proportional to their respective heights. Hence, let's find the scale factor by comparing the length of the yardstick's shadow to its actual length:

Scale factor = Length of the yardstick's shadow / Length of the yardstick
= 21 inches / 36 inches

Step 2: Calculate the height of the building
Now we can use the scale factor to find the height of the building. We know that the length of the building's shadow is 168 feet. Since we need the height in feet, let's convert the yardstick's length from inches to feet:

Length of the yardstick = 36 inches * (1 foot / 12 inches)

Height of the building = Length of the building's shadow * Scale factor
= 168 feet * (Length of the yardstick / Length of the yardstick's shadow)
= 168 feet * (36 inches / 21 inches) * (1 foot / 12 inches)

Simplifying the expression, we get:

Height of the building = 168 feet * (36 / 21) * (1 / 12)
= 72 feet

Therefore, the height of the building is 72 feet.

36 inches = 3 feet

21 inches = 1.75 feet

3/1.75 = x / 168

Cross multiply and solve for x.