Question

the length of a buildings shadow is 20 meters at the same time that a 2 - meter stick casts a shadow of 4 meters. using similar triangles, what is the height of the building?
a. 15 meters
b. 10 meters
c. 20 meters
d. 5 meters

a flagpole creates a right triangle with the ground. the flagpole is 20 feet tall, and the shadow is 15 feet long. what is the distance from the top of the flagpole to the tip of the shadow?
a. 30 ft
b. 25 ft
c. 40 ft
d. 35 ft

Explanation:

Step1: Set up proportion for building height

Let the height of the building be $h$. Since the triangles are similar, the ratios of corresponding sides are equal. So we have $\frac{h}{20}=\frac{2}{4}$.

Step2: Solve for $h$

Cross - multiply: $4h = 2\times20$, then $4h=40$. Divide both sides by 4: $h = 10$ meters.

Step3: Use Pythagorean theorem for flag - pole problem

Let the distance from the top of the flag - pole to the tip of the shadow be $d$. By the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $a = 20$ (height of flag - pole) and $b = 15$ (length of shadow). So $d=\sqrt{20^{2}+15^{2}}=\sqrt{400 + 225}=\sqrt{625}=25$ feet.

Answer:

1. b. 10 meters
2. b. 25 ft