1. On a trip to Washington D.C., you and your friend are standing next to the Washington Monument. Your friend wants to buy a guide book to find out how tall the Washington Monument is, but will use the money to buy a snack to share instead if you can figure it out. If you already know your own height, what two additional measurements must you know to solve the problem? Select the two correct measurements below.
A. The length of the shadow cast by the Washington Monument
B. The length of the shadow cast by the Lincoln Memorial
C. The length of your friend's shadow
D. The length of your shadow
2. If a 30 foot tall tree casts an 18 foot shadow, determine the height of a nearby tree that casts a 24 foot shadow. Round to the nearest tenth if needed.
The tree is----------- feet tall.
3. Determine if the triangles below are similar. If so, write a similarity statement.
A. Yes, the triangles are similar. △PSQ∼△SRT
B. No, the triangles are similar.
C. Yes, the triangles are similar. △PSQ∼△RST
D. Yes, the triangles are similar. △PSQ∼△TSR
4. Is the following solution for the value of x in the figure correct or incorrect? Explain
4/8=15/x
4x=120
X=30
A. The solution for the value of x is incorrect because the value of x is calculated incorrectly when solving the proportion.
B. The solution for the value of x is correct because the value of x is calculated by taking the correct proportion.
C. The solution for the value of x is incorrect because the proportion does not use the ratios of corresponding sides.
D. The solution for the value of x is incorrect because the triangles are not similar, so the proportion is not valid.
5. In △ABC, m∠A=42°, m∠B=50°, AB=4, and AC=3.
In △XYZ, m∠X=42°, m∠Z=88°, XY=14, and YZ=9.5.
Determine the measures of BC¯¯¯¯¯¯¯¯ and XZ¯¯¯¯¯¯¯¯ . Round to one decimal place.
BC=----------,XZ=
2
2.7
7.1
10.5
1. The correct measurements to solve the problem are A. The length of the shadow cast by the Washington Monument and D. The length of your own shadow.
2. To solve this problem, we can use the proportion method. If the height and shadow are proportional, we can set up the following equation:
30 feet / 18 feet = x feet / 24 feet.
Solving for x, we get x = (30/18) * 24 = 40 feet.
Therefore, the nearby tree is 40 feet tall.
3. The correct answer is C. Yes, the triangles are similar. △PSQ∼△RST. This is because the angles are congruent (both have a 90 degree angle and a 41 degree angle), and the sides are proportional (PS/RT = 5/4, SQ/ST = 3/2, PQ/RS = 4/5).
4. The correct answer is A. The solution for the value of x is incorrect because the value of x is calculated incorrectly when solving the proportion. The correct equation should be: 4/8 = 15/x, which simplifies to 1/2 = 15/x. Cross multiplying, we get 2x = 15, so x = 7.5. The solution of x = 30 is incorrect.
5. To solve this problem, we can use the Law of Sines.
For triangle ABC: BC/sin(B) = AC/sin(A),
BC/sin(50) = 3/sin(42),
BC = (sin(50)/sin(42)) * 3 ≈ 3.7.
For triangle XYZ: XZ/sin(Z) = YZ/sin(X),
XZ/sin(88) = 9.5/sin(42),
XZ = (sin(88)/sin(42)) * 9.5 ≈ 10.5.
Therefore, BC ≈ 3.7 and XZ ≈ 10.5.