Solving Similar Right Triangles: Diagrams and Word Problems

Susan is flying a kite, which gets caught in the top of a tree.  Use the diagram to estimate the height of the tree. 

• 63 ft

• 65 ft

• 74 ft

• 87 ft

You need a ladder that will reach up a 25 foot tall house when placed 10 feet away from the house. How tall does the ladder need to be?

• 25 feet

• 26 feet

• 27 feet

• 28 feet

The foot of a ladder is placed 6 feet from a wall. If the top of the ladder rests 8 feet up on the wall, how long is the ladder?

• 10 ft

• 14 ft

• 17 ft

• 100 ft

Find, to the nearest degree, the angle which the sun's rays make with the ground when a flagpole 40 feet high casts a shadow 30 feet long.

• 48^o

• 37^o

• 28^o

• 53^o

The two right triangles below are similar. What is x, the missing side length in triangle DEF? 

• 3.75

• 9.75

• 10

• 12

The two right triangles below are similar. What is x, the missing side length in triangle DEF? 

• 3.75

• 9.75

• 10

• 12

What is the size of angle x and the length of sides y and z?

• x = 63, y = 2.5, z = 9.6

• x = 63, y = 6.4, z = 3.75

• x = 97, y = 6.4, z = 9.6

• x = 97, y = 2.5, z = 3.75

Hint: type a proportion into desmos :)

• a

• b

• c

• d

Find the length of side y.

• 22.32 cm

• 36.5 cm

• 76.34 cm

• 87.76 cm

What is the length of side x?

• 6.57 cm

• 7 cm

• 7.44 cm

• 26.33 cm