No. 40.
607
MENSURATION,
CLASS I.
1. By what method can you find the area of a triangle having given the length of the three sides?
2. Prove that the volume of a sphere
=
r.
3. Find the area of a field from the following entry in a field hook :-
To D
538
To C 66
400
From B
on left.
To B
629
To D 295
179
From A
go East.
4. The minute haud of a clock is 65 inches long, find the area on the clock face which it describes between 12 and 12.40 o'clock.
No. 41.
MENSURATION.
CLASS II.
1. How long must a fire escape be to reach from the middle of a street 50 feet wide to the top of the front wall of a house 60 feet high?
2. What are similar figures? Give an example.
3. Having given the chord of an are, and the height of the are, show by rule and example how to find the diameter of the circle.
4. The chord of half an are is 12 feet, and the diameter of the circle is 80 feet: find the chord of the are.
No. 42.
TRIGONOMETRY.
SENIOR.
1. If a street runs due North and South and the height of the houses on each side is equal and such that a line drawn from the top of the front wall of any house to the foot of the wall of the house exactly opposite makes au angle of 60° with the roadway, for how many hours per day conld sunshine get down to the roadway supposing the sun to rise due East and set due West?
2. Prove that cod A-cot 2 A=cos:c 2 A.
3. Show how to solve a triangle having given two angles and a side.
4. In a triangle A B C the angle at B=45° and that at C=75°, and the shortest distance between the angle A and the side B C=3 inches, what are the respective lengths of the sides of the triangle?
5. What is a logarithun? Show that the logarithm of a product equals the sum of the logarithms of its factors.