Lesson 2

Example

 

A roof truss is built with a slope of 2.5:12. What is the vertical height of the truss in the diagram? Round your answer to one decimal place.

 

 

Solution

 

The two right triangles representing the slope and the truss are similar because the truss must have the same slope. Corresponding sides will have the same ratios and, therefore, all the angles will be equal.   Let x be the height of the truss.   Set up a proportion for the corresponding sides of the triangles.
Solve the proportion.   The height is approximately 2.1 ft or 2 ft 1 in.

 

Self-Check 1

 

1. A wheelchair ramp is 30 m long, and its bottom is 1.5 m below the top of the ramp.
   
   
   1. How far is a wheelchair above the foot of the ramp when it is 10 m from the top of the ramp? Answer
      
      
   2. What is the slope of the ramp? Round your answer to two decimal places. Answer

2. Vanaja is standing on the east bank of the South Saskatchewan River in Saskatoon. She looks at the historic Bessborough Hotel on the opposite shore and wonders how far away the building is. Vanaja walks 150 m downstream along the bank and stops and places a stick, S, in the bank. Then she walks 30 m further downstream. She turns 90° and walks 20 m away from the river until she sees that the stick she placed on the bank lines up with the hotel across the river. Calculate the original distance, x, that Vanaja was from the hotel.
   
   
   
   Answer
   
   

3. A timber is positioned 30 cm from the end of a 2-m steel bar. The free end of the bar is lifted 20 cm. To the nearest centimetre, how high is the timber off the ground?
   
   
   
   Answer
   
   
4. The foot of a 20-ft ladder is located 5 ft from a vertical wall. A painter is standing 16 ft above the foot of the ladder. How far from the wall is he?
   
   
   iStockphoto/Thinkstock
   
   Answer