Surveyors wished to know the distance across a lake between A and B. They measured the distance from B to C as 100 m and the ang
le from C to A to be 55°. Knowing that the angle between CB and BA was 90°, they used trig to solve for the distance. Show how it was done
1 answer:
Answer:
<h3>AB ≈ 70m</h3>Step-by-step explanation:
Check the attachment for the diagram.
You can see from the diagram that it is a right angled triangle with opposite side AB and adjacent side BC. Using SOH, CAH, TOA trig identity to get the length of AB. According to TOA;
tan 35° = opposite/adjacent
tan 35° = AB/BC
tan 35° = AB/100
AB = 100tan35°
AB = 100 * 0.7002
AB = 70.02m
Hence the distance across a lake between A and B is approximately 70m
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We will proceed to solve each case to determine the solution of the problem.
<u>case a)</u>
Group terms that contain the same variable, and move the constant to the opposite side of the equation
Complete the square. Remember to balance the equation by adding the same constants to each side.
Rewrite as perfect squares
therefore
case a) is not the solution of the problem
<u>case b)</u>
Group terms that contain the same variable, and move the constant to the opposite side of the equation
Complete the square. Remember to balance the equation by adding the same constants to each side.
Rewrite as perfect squares
therefore
case b) is not the solution of the problem
<u>case c)</u>
Group terms that contain the same variable, and move the constant to the opposite side of the equation
Complete the square. Remember to balance the equation by adding the same constants to each side.
Rewrite as perfect squares
therefore
case c) is not the solution of the problem
<u>case d)</u>
Group terms that contain the same variable, and move the constant to the opposite side of the equation
Complete the square. Remember to balance the equation by adding the same constants to each side.
Rewrite as perfect squares
therefore
case d) is the solution of the problem
therefore
<u>the answer is</u>