Forest Belton forestbelton

Problem

Find the length $d$ in

Classical solution

Let the angles of $A_1$ and $B$ be $\alpha$ and $\beta$ respectively, as shown in the Figure 1.6. The law of cosines in the triangle $\overline{A_1 A_2 A_3}$ gives

$$4^2 = 5^2 + 6^2 - 2 \times 5 \times 6 \times \cos{\alpha}$$

	% A keypad lock on a door has a code of five different digits. Can you use the six clues below to determine the correct code to get in?
	%
	% 1. There are no zeroes in the five-digit code.
	% 2. The first digit is smaller than the second digit.
	% 3. Exactly two of the five digits are odd.
	% 4. The middile digit is a perfect square.
	% 5. The two-digit number formed by the fourth and fifth digits is a perfect square.
	% 6. The two-digit number formed by the third and fourth digits is equal to the first digit multiplied by ythe second digit.
	is_digit(1).
	is_digit(2).

	function awkn {
	local ARGS=""
	local FLAG=""

	local N="$1"
	shift

	while getopts "F:v:" FLAG; do
	case "$FLAG" in
	F) ARGS="$ARGS -F$OPTARG" ;;

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