Also, use tables and not
calculators. Finally, do not forget your units.
1. A ladder 20 METRES long rests against a vertical wall. The distance between the foot
of the ladder and the wall is 9 METERS
a. Find, correct to the nearest degree, the angle that the ladder makes with
the wall.
b. Find, correct to 1 decimal place, the height above the ground at which
the upper end of the ladder touches the wall.
............ and by my Sea Scout Ship.
(a) cosθ = 9/20
(b) h^2 + 9^2 = 20^2
you mean you have tables for cosines and square roots?
Who uses tables any more?
Why did this remind me of an old TV show by Roy Underhill, called The Woodwright's Shop?
They did woodworking using only vintage, muscle-powered and hand-tools.
I used tables, but then that was 1958! And apparently, tables are still used in Lagos.
So, how's it coming with that sextant?
a. sin A = 9/20
A = 27 deg.
b. Cos 27 = h/20
h = 17.8 meters.
To find the angle that the ladder makes with the wall, you can use the trigonometric function "arctan" (also known as "tan^(-1)").
a. To find the angle:
Step 1: Identify the given information:
- Length of the ladder = 20 meters
- Distance between the foot of the ladder and the wall = 9 meters
Step 2: Define the trigonometric relationship:
The tangent of an angle is defined as the ratio of the opposite side (height) to the adjacent side (distance between the foot and the wall). Therefore, we can use the tangent function (tan) to find the angle.
Step 3: Apply the formula:
The formula to find the angle using the tangent function is: angle = arctan(opposite / adjacent)
In this case, the opposite side (height) is the unknown, while the adjacent side is the given distance between the foot and the wall. So we can rewrite the formula as:
angle = arctan(height / 9)
Step 4: Calculate the angle using a table:
You can use a table of common trigonometric values to find the angle. Look up the value of arctan(height / 9) in the table, and the corresponding angle will be your answer. Make sure to round the angle to the nearest degree, as per the given instructions.
Note: Since we don't know the height yet, we cannot calculate the angle accurately. We need the height value to proceed.
b. To find the height at which the upper end of the ladder touches the wall:
Step 1: Use the Pythagorean theorem:
The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the ladder's length) is equal to the sum of the squares of the other two sides.
In this case, the hypotenuse (ladder) is 20 meters long, and one side is the distance between the foot and the wall (9 meters). Let's assume the height is h.
According to the theorem, we have:
20^2 = 9^2 + h^2
Step 2: Solve for h:
Rearrange the equation to solve for h:
h^2 = 20^2 - 9^2
h^2 = 400 - 81
h^2 = 319
h = √(319)
Step 3: Calculate the height using a table or calculator:
Using a calculator or estimation method, find the square root of 319 (√(319)). Round the value to one decimal place, as per the given instructions. The resulting value will give you the height at which the upper end of the ladder touches the wall.
Note: It is essential to follow the instructions and use tables instead of calculators for the calculations, as mentioned in the problem. However, for accurate and efficient calculations, using calculators or computer tools is recommended.