Question

a building casts a shadow of 20 meters, while a 5 - meter pole casts a shadow of 2 meters at the same time. what is the height of the building?
a. 40 meters
b. 30 meters
c. 50 meters
d. 25 meters

a triangular roof truss has side lengths of 9 feet, 12 feet, and 15 feet. another roof truss is designed with side lengths of 6 feet, 9 feet, and 10 feet. are the two trusses similar?
a. no, the sides are not proportional
b. yes, by the sas criterion
c. no, the angles do not match
d. yes, by the sss criterion

Explanation:

Step1: Set up proportion for building - pole problem

Let the height of the building be $h$. Since the ratios of object - height to shadow - length are equal at the same time, we have the proportion $\frac{h}{20}=\frac{5}{2}$.

Step2: Solve the proportion for $h$

Cross - multiply: $2h = 5\times20$. Then $2h=100$, and $h = 50$ meters.

Step3: Check similarity of triangles

For the two triangular roof trusses, check the ratios of corresponding sides. $\frac{6}{9}=\frac{2}{3}$, $\frac{9}{12}=\frac{3}{4}$, $\frac{10}{15}=\frac{2}{3}$. Since the ratios of the corresponding sides are not all equal (i.e., $\frac{2}{3}
eq\frac{3}{4}$), the sides are not proportional.

Answer:

1. c. 50 meters
2. a. No, the sides are not proportional