Before we use Sketchpad to help us solve this problem, let's
take a trip to the hardware store.
At the store they sell a couple different types of ladders.
They don't sell them 100 ft long, so we'll have to custom order it. You
find out that it costs 2$/ft for the ladder. Also, you read a label on
a ladder that says
The ladder can only be safely used if the angle of the
ladder to the ground is no more than 75 degrees!. This can be
demonstrated by the picture below.
Notice how the ladder, building and ground make up three sides
of a triangle.
To do this part of the lesson, download this
Geometer's
Sketchpad file.
Open the Sketchpad file and follow the following steps.
The first thing we need to is to make the angle the ladder
forms with the ground to 75 degrees.
STEP 1: MEASURE < BCA (SELECT the points B, C and A
in order and go to the MEASURE menu and select ANGLE.
Write down your measurement.
STEP 2: SELECT and MOVE point C so that the angle you
just measured is 75 degrees.
We now know the angle measure and one side (the height of the
building). Using trigonometry we can now find every angle and side in
the triangle.
STEP 3: Double-click the SHOW button on the top of the
screen. This will tell you the LENGTH of the LADDER for a 75 degree
angle.
Write down the answer.
STEP 4: Select BOTH the measurements (the ladder and
the building) and go the menu MEASURE and select CALCULATE....
STEP 5: Under VALUES select the length of the
building and then click / (for divide) and finally under
values select the length of ladder .
Click OK. Write down your answer
STEP 6: Next, select the angle measurement you found in
STEP 1. Under the MEASURE menu, select CALCULATE.....
STEP 7: Under FUNCTIONS select the option SIN(
and then under VALUES select < BCA . Click OK. Write down
your answer.
STEP 8: What do you notice about the ration you
calculated and the SIN of the angle?
It is common to label the sides of a triangle as in the figure
below.
NOTE that the side names are dependent on the angle you are
considering except for the HYPOTENUSE which is always the side across
from the right angle.
STEP 9: Write a ratio using the names of the sides in
the picture above to describe the SIN of < BAC.
SIN of < BCA =
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Problem Statement- -Go to Lesson
Worksheet 2-