Geometry and Indirect Measure
20 ft. tall
The boy in the figure is 5 ft. tall and his shadow is 4 ft. If the shadow of the flagpole is 16 ft., determine the height of the flagpole.
Length of CB = 48 Ratio of CE to CB = 1/3 Length of AC = 36 Length of AB = 60
A surveyor put stakes at the lettered points. He used string to determine lengths of line segments and to check that lines ACE and BCD form right angles at C. DC = 12, CE = 16, DE = 20, DB = 60 CE/CB = DC/AC = DE/AB
AB/4 = 15/3 AB = 20 units.
Answer the following questions based on the graphic and information given below. In the figure below a surveyor put stakes at the lettered points. He used string to determine lengths of line segments and a transit to check that the angles at D and B were both right angles. If CD = 3, CE = 5, DE = 4, DB = 18, and AB/DE = BC/CD Fill in the provided proportion with the appropriate numerical values and solve for the missing side value. Enter the proportion values and correct answer in the spaces provided.
3 15 3 to 15 2
Answer the following questions based on the graphic given below. The person casts a shadow ____ feet long. The building casts a shadow _____ feet long. The ratio of the person's shadow to the building's shadow is ____ to _____.If the other side of the building is 10 feet tall, the person will be _____ feet tall.
60
A triangle has three angles with equal measures. What is the measure of each angle?
30 and 60
Solve this problem. Two angles are complementary. One contains 30° more than the other. Find both angles. The measures of the angles are ______ and ______ degrees.
54 and 72
Two angles of a triangle have equal measures, but the third angle's measure is 36° less than the sum of the other two. Find the measure of each angle of the triangle. The first and second angles measure ______ degrees, and the third angle measures ______ degrees
cosine 0.6428 x 90 45 30
A surveyor wants to know the distance from the top of the tower to the bottom of the tower. Round trigonometric functions to four decimal places. If the angle at the top of the tower is known, a surveyor would use the ______function to find the length x. The cosine of a 50° angle is _______; this represents the value created when length _____ is divided by _____ feet. If the angle near the top of the tower was changed to 60°, the cosine would be 0.5; now the length of x would be ______ feet. If the angle near the top of the tower was changed to 60°, the angle from the light and the ground would be _____ degrees.
39 degrees
How large is an angle whose supplement contains 12° less than three times its complement?
38° and 52°
An angle is 14° more than the measure of its complement. Find the measure of each angle.
52° and 128°
An angle measures 24° more than twice its supplement. Find the measure of the supplementary angles.
x = 13 1/3 ft.
Make a sketch if you need to and solve this problem using similar triangles. A telephone pole has a shadow of 16 ft. when a person 5 ft. tall has a shadow of 6 ft. How tall is the pole? Write answer as a mixed number.
similar flagpole flagpole
Use the graphic to complete each sentence. Remember to spell correctly. If you want to find the height of an object like a flagpole, you can use _____ triangles. Line segment DC is the height of the _____. Using the length of BE (the boy's height), AB (the boy's shadow), and AC (the shadow of flagpole), you can use a proportion to determine the height of the _______.
